diff --git a/kotlin-native/runtime/src/custom_alloc/README.md b/kotlin-native/runtime/src/custom_alloc/README.md
new file mode 100644
index 00000000000..0b0e323eeb3
--- /dev/null
+++ b/kotlin-native/runtime/src/custom_alloc/README.md
@@ -0,0 +1,357 @@
+# Overview of the allocator
+
+This document describes the internals of the custom allocator. The presentation
+here is not fully true to the implementation, as the design is still work in
+progress.
+
+The main idea of the custom allocator is to divide system memory into chunks
+(pages) that each can be swept independently, in memory consecutive order.
+Every allocation ends up as a block of memory inside a page. Each page keeps
+track of the size of each block it contains; how this is done depends on the
+page type, with different page types optimized for different allocation sizes.
+All the memory blocks are consecutive within a page, so the size of a block
+also tells where the next block begins. Paired with an additional mechanism
+(page type dependent) for determining whether a block is allocated, we can
+iterate through the allocated blocks.
+
+When a thread allocates memory for an object, it will find a page suitable for
+the given allocation size. Each thread holds on to a number of pages for the
+different size categories. The typical case is that the thread’s current page
+for the given size can fit the requested allocation. If that is not the case, a
+different page for that size category is requested from the shared allocation
+space. The requested page can either be readily available (already prepared by
+the GC thread), or it might need to be swept first, or it might be newly
+created.
+
+The GC thread has a new responsibility when using this allocator: While the
+mutator threads are paused at the start of GC, the GC thread must prepare the
+allocator for sweeping. This does two things. First, it marks all pages as
+“needs to be swept before next use”. Second, it releases pages that threads are
+holding on to, by clearing the thread local variables for each thread.
+
+It is possible to have several independent allocation spaces at the same time.
+This is currently useful for testing, but is potentially useful in other
+settings.
+
+# Detailed Design
+
+All allocations are made through a `CustomAllocator` object.
+
+## [CustomAllocator](cpp/CustomAllocator.hpp)
+
+```cpp
+class CustomAllocator {
+public:
+    CustomAllocator(Heap& heap, GCSchedulerThreadData& scheduler);
+    ObjectHeader* CreateObject(TypeInfo* type);
+    ArrayHeader* CreateArray(TypeInfo* type, uint32_t count);
+    ExtraObjectData* CreateExtraObject();
+    void PrepareForGc();
+
+private:
+    uint8_t* Allocate(uint64_t cellCount);
+    uint8_t* AllocateInSingleObjectPage(uint64_t cellCount);
+    uint8_t* AllocateInNextFitPage(uint32_t cellCount);
+    uint8_t* AllocateInFixedBlockPage(uint32_t cellCount);
+
+    Heap& heap_;
+    GCSchedulerThreadData& gcScheduler_;
+    NextFitPage* nextFitPage_;
+    FixedBlockPage* fixedBlockPages_[MAX_BLOCK_SIZE];
+    ExtraObjectPage* extraObjectPage_;
+};
+```
+
+The primary responsibility of this class is to delegate each requested
+allocation to pages of the appropriate type, based on allocation size. To do
+this, it requests pages from the shared allocation space (`Heap`) and stores
+pages for later allocations. Each thread thus owns a number of pages for
+different allocation sizes, but at most one for each size class. When
+allocating, the `CustomAllocator` will first try to allocate in one of its
+owned pages. If this fails, it will request a new page for that size class from
+a shared `Heap` object. `SingleObjectPages` are never kept by the
+`CustomAllocator`, since they are created specifically for a single allocation,
+with no extra space.
+
+## [Heap](cpp/Heap.hpp)
+
+```cpp
+class Heap {
+public:
+    void PrepareForGC();
+
+    void Sweep();
+
+    AtomicStack<ExtraObjectCell> SweepExtraObjects(GCHandle gcHandle);
+
+    FixedBlockPage* GetFixedBlockPage(uint32_t cellCount);
+    NextFitPage* GetNextFitPage(uint32_t cellCount);
+    SingleObjectPage* GetSingleObjectPage(uint64_t cellCount);
+    ExtraObjectPage* GetExtraObjectPage();
+
+private:
+    PageStore<FixedBlockPage> fixedBlockPages_[MAX_BLOCK_SIZE];
+    PageStore<NextFitPage> nextFitPages_;
+    PageStore<SingleObjectPage> singleObjectPages_;
+    AtomicStack<ExtraObjectPage> extraObjectPages_;
+    AtomicStack<ExtraObjectPage> usedExtraObjectPages_;
+};
+```
+
+A `Heap` object represents a shared allocation space for multiple
+`CustomAllocator`s, which can request pages through one of the
+`GetFixedBlockPage`, `GetNextFitPage`, `GetSingleObjectPage` methods. It also
+provides a method for sweeping through all blocks that have been allocated in
+this heap. The `Heap` object is the synchronization point, and guarantees that
+every page is returned at most once. Page ownership is thus implicitly given to
+the thread that called the method. The `Heap` object keeps track of all pages,
+so there is no need to explicitly return ownership of a page.  Internally, a
+`Heap` keeps the pages for each size class in a `PageStore`. This means one for
+`SingleObjectPage`s, one for `NextFitPage`s, one for each of the block sizes
+for `FixedBlockPage`s. `ExtraObjectPage`s are stored directly in two
+`AtomicStack`s, since they require different handling during sweeping.
+
+## [PageStore](cpp/PageStore.hpp)
+
+```cpp
+template <class PageType>
+class PageStore {
+public:
+    void PrepareForGC();
+    void Sweep();
+    void SweepAndFree();
+    PageType* GetPage(uint32_t cellCount);
+    PageType* NewPage(uint64_t cellCount);
+
+private:
+    AtomicStack<PageType> empty_;
+    AtomicStack<PageType> ready_;
+    AtomicStack<PageType> used_;
+    AtomicStack<PageType> unswept_;
+};
+```
+
+A PageStore is responsible for keeping track of all pages of a given type and
+size class. Each of the pages are in one of four stacks. The stack, that a
+given page is in, determines its current state:
+
+* `unswept_`: have not yet been swept since the last GC cycle.
+* `ready_`: are ready for allocation; has been swept by the GC thread.
+* `used_`: has been given to some thread for allocation; it might still be used
+    for allocation, or it might have been discarded with not enough space left.
+    Will not be used until the next GC cycle.
+* `empty_`: same as `ready_`, but does not contain any objects. Will be freed
+    before the next GC, if not needed before then.
+
+When a page is requested, the page is taken from `ready_`, if there are any.
+Otherwise, an `unswept_` page is taken and swept before returning. If there are
+no unswept pages either, an empty page is taken, if there are any. Otherwise a
+new page is created in the size category. All returned pages are moved to
+`used_`. During the marking phase, all remaining pages in `empty_` are freed,
+and all other pages are moved to `unswept_`. The GC thread will go through all
+`PageStore`s and sweep the pages in `unswept_` and move them to `ready_`. If one
+of the other threads sweeps a page from `unswept_`, it is moved directly to
+`used_`, as it is claimed by the `CustomAllocator` that swept it.
+
+`SingleObjectPage`s are treated slightly differently, because they are created
+for one specific single allocation, and not reused when that allocation is
+freed. A `SingleObjectPage` allocation goes directly to `NewPage(...)`, without
+checking any of the stacks, and during sweeping, they are freed directly rather
+than being put into the `empty_` stack. Ideally, there would only be two stacks
+in play for `SingleObjectPages`; `used_` and `unswept_`. However, very little
+is lost by just using the existing `PageStore` logic used for the other pages.
+
+## [AtomicStack](cpp/AtomicStack.hpp)
+
+```cpp
+template <class PageType>
+class AtomicStack {
+public:
+    PageType* Pop();
+    void Push(PageType* elm);
+    void TransferAllFrom(AtomicStack<T>& src);
+    bool isEmpty();
+
+
+private:
+    std::atomic<PageType*> stack_;
+};
+```
+
+The only place where atomics are used are in the stacks inside the `PageStore`.
+All page classes have a non-atomic next pointer, to be used for linking up in
+exactly one stack. `Pop` and `Push` are implemented with compare-and-swap
+operations. The class is thread safe, except for if an element is freed while
+another thread tries to Pop it from a stack.
+
+# Page types
+
+This section is likely to change, given the likely introduction of additional
+page types. It also describes some details about which page type is chosen for
+a given allocation, which is also likely to change.
+
+There are four different page types, but they all share the feature that they
+can be swept independently. The Sweep methods return whether there were any
+live objects in the page after sweeping. If not, the page will be given back to
+the OS.
+
+## [FixedBlockPage](cpp/FixedBlockPage.hpp)
+
+```cpp
+class FixedBlockPage {
+public:
+    FixedBlockPage(uint32_t blockSize);
+    uint8_t* TryAllocate();
+    bool Sweep() noexcept;
+
+private:
+    FixedBlockPage* next_; // used by AtomicStack
+    uint32_t blockSize_;
+    FixedBlockCell* nextFree_;
+    FixedBlockCell cells_[];
+};
+```
+
+All sufficiently small allocations (currently arbitrary <1KiB) are directed to
+a `FixedBlockPage`, where all blocks have the same fixed size. Most allocations
+are expected to be in this page type. A `FixedBlockPage` has a singly-linked
+free-list of all free blocks. Allocating always happens in the first free block
+in the page.
+
+```cpp
+struct FixedBlockCell {
+    union {
+        uint8_t data[];
+        FixedBlockCell* nextFree;
+    }
+};
+```
+
+The important point is that all links in the list point forward in the page, so
+all blocks between two consecutive links are implicitly allocated. Sweeping a
+`FixedBlockPage` consists of walking the free-list forward, and sweeping all
+blocks in between the links, maintaining the free list when blocks are freed.
+
+Each small page takes up the same amount of space, independent of block size,
+so larger block size implies fewer blocks per page.  This size is arbitrarily
+chosen to be 64 KiB, but this might change.
+
+## [NextFitPage](cpp/NextFitPage.hpp)
+
+```cpp
+class NextFitPage {
+public:
+    NextFitPage(uint32_t cellCount);
+    Cell* TryAllocate(uint32_t cellCount);
+    bool Sweep();
+
+private:
+    NextFitPage* next_; // used by AtomicStack
+    Cell* curBlock_;
+    Cell cells_[];
+};
+```
+
+Allocations that could theoretically fit in a `FixedBlockPage`, but would
+require too large a block size (arbitrary >=1KiB), are allocated in a
+`NextFitPage`. `NextFitPage`s are the same size as `FixedBlockPage`s (arbitrary 64
+KiB for experiments). All blocks in a `NextFitPage` have a header that tells how
+big the block is, and whether it is allocated or not. There are no gaps between
+blocks, so the size of a block also tells where the next block is. The header
+information fits inside a 8 byte `Cell`.
+
+```cpp
+class Cell {
+public:
+    Cell(uint32_t size);
+    uint8_t* TryAllocate(uint32_t cellCount);
+
+private:
+    uint32_t isAllocated_;
+    uint32_t size_;
+    uint8_t data_[];
+};
+```
+
+The page keeps a reference to a currently active block, and will try to bump
+allocate inside that block. If allocation does not fit, we move to the next
+block that fits. If no block in the page fits the requested size, the page is
+abandoned until the next GC.
+
+## [SingleObjectPage](cpp/SingleObjectPage.hpp)
+
+```cpp
+class SingleObjectPage {
+public:
+    SingleObjectPage(uint64_t cellCount);
+    bool Sweep();
+
+private:
+    SingleObjectPage* next_; // used by AtomicStack
+};
+```
+
+Allocations too big for a `NextFitPage` are allocated in a `SingleObjectPage`,
+which only contains that single block of the requested size. They are also
+handled slightly differently by both `Heap` and `CustomAllocator`. First off,
+`Heap::GetSingleObjectPage` will never check existing pages, and instead just
+allocate a new page. Secondly, a `CustomAllocator` does not keep a reference to
+any of the `SingleObjectPage`s. As a consequence, they are only swept by the GC
+thread.
+
+## [ExtraObjectPage](cpp/ExtraObjectPage.hpp)
+
+```cpp
+class ExtraObjectPage {
+public:
+    ExtraObjectPage();
+    ExtraObjectData* TryAllocate();
+    bool Sweep(FinalizerQueue& queue);
+
+
+private:
+    ExtraObjectPage* next_; // used by AtomicStack
+    ExtraObjectCell* nextFree_;
+    ExtraObjectCell cells_[];
+};
+```
+
+Extra objects are used for attaching additional data to some objects. This is
+used for objects that require special handling during garbage collection:
+
+* objects with finalizers
+* weak references
+* interop references
+
+Extra objects are allocated in `ExtraObjectPage`s, which are very similar to
+`FixedBlockPage`s. They primarily differ in how they are swept, since it is
+during sweeping of `ExtraObject`s that scheduling of finalization happens. If
+an object that requires finalization is found, it is added to the
+`FinalizerQueue` given as argument. The cells are also slightly different, in
+that they add a new field that allows the cells to be added to the finalizer
+queue.
+
+```cpp
+struct ExtraObjectCell {
+    ExtraObjectCell* next_; // used by AtomicStack
+    ExtraObjectData data_;
+};
+```
+
+# Finalizers
+
+Section like to change.
+
+In the existing memory model, finalization tasks are found and scheduled during
+sweeping of regular objects. The objects to be finalized are chained together
+using a pointer in the Node header, added to all allocated objects. This header
+is not needed in the custom allocator, apart from linking in the finalization
+queue.
+
+We therefore reintroduce this pointer in a header for `ExtraObjectData`. For
+this, we reuse the `ExtraObjectCell` as header for both free list pointer and as
+linking pointer for the `AtomicStack` that we use as the `FinalizerQueue`.
+
+# Enabling the allocator
+
+The custom allocator is enabled with the compiler flag -Xallocator=custom.
diff --git a/kotlin-native/runtime/src/custom_alloc/cpp/Cell.hpp b/kotlin-native/runtime/src/custom_alloc/cpp/Cell.hpp
index b37aa9f5352..81f7141247e 100644
--- a/kotlin-native/runtime/src/custom_alloc/cpp/Cell.hpp
+++ b/kotlin-native/runtime/src/custom_alloc/cpp/Cell.hpp
@@ -27,7 +27,7 @@ public:
     Cell* Next() noexcept;
 
 private:
-    friend class MediumPage;
+    friend class NextFitPage;
 
     uint32_t isAllocated_;
     uint32_t size_;
diff --git a/kotlin-native/runtime/src/custom_alloc/cpp/CustomAllocConstants.hpp b/kotlin-native/runtime/src/custom_alloc/cpp/CustomAllocConstants.hpp
index a046f46f2b9..6fc90e7b851 100644
--- a/kotlin-native/runtime/src/custom_alloc/cpp/CustomAllocConstants.hpp
+++ b/kotlin-native/runtime/src/custom_alloc/cpp/CustomAllocConstants.hpp
@@ -9,23 +9,23 @@
 #include <cstddef>
 #include <cstdint>
 
-#include "SmallPage.hpp"
-#include "MediumPage.hpp"
+#include "FixedBlockPage.hpp"
+#include "NextFitPage.hpp"
 #include "ExtraObjectPage.hpp"
 
 inline constexpr const size_t KiB = 1024;
 
-inline constexpr const size_t SMALL_PAGE_SIZE = (256 * KiB);
-inline constexpr const int SMALL_PAGE_MAX_BLOCK_SIZE = 128;
-inline constexpr const size_t SMALL_PAGE_CELL_COUNT =
-        ((SMALL_PAGE_SIZE - sizeof(kotlin::alloc::SmallPage)) / sizeof(kotlin::alloc::SmallCell));
+inline constexpr const size_t FIXED_BLOCK_PAGE_SIZE = (256 * KiB);
+inline constexpr const int FIXED_BLOCK_PAGE_MAX_BLOCK_SIZE = 128;
+inline constexpr const size_t FIXED_BLOCK_PAGE_CELL_COUNT =
+        ((FIXED_BLOCK_PAGE_SIZE - sizeof(kotlin::alloc::FixedBlockPage)) / sizeof(kotlin::alloc::FixedBlockCell));
 
-inline constexpr const size_t MEDIUM_PAGE_SIZE = (256 * KiB);
-inline constexpr const size_t MEDIUM_PAGE_CELL_COUNT =
-        ((MEDIUM_PAGE_SIZE - sizeof(kotlin::alloc::MediumPage)) / sizeof(kotlin::alloc::Cell));
+inline constexpr const size_t NEXT_FIT_PAGE_SIZE = (256 * KiB);
+inline constexpr const size_t NEXT_FIT_PAGE_CELL_COUNT =
+        ((NEXT_FIT_PAGE_SIZE - sizeof(kotlin::alloc::NextFitPage)) / sizeof(kotlin::alloc::Cell));
 
-// MEDIUM_PAGE_CELL_COUNT minus one cell for header minus another for the 0-sized dummy block at cells_[0]
-inline constexpr const size_t MEDIUM_PAGE_MAX_BLOCK_SIZE = (MEDIUM_PAGE_CELL_COUNT - 2);
+// NEXT_FIT_PAGE_CELL_COUNT minus one cell for header minus another for the 0-sized dummy block at cells_[0]
+inline constexpr const size_t NEXT_FIT_PAGE_MAX_BLOCK_SIZE = (NEXT_FIT_PAGE_CELL_COUNT - 2);
 
 inline constexpr const size_t EXTRA_OBJECT_PAGE_SIZE = 64 * KiB;
 inline constexpr const int EXTRA_OBJECT_COUNT =
diff --git a/kotlin-native/runtime/src/custom_alloc/cpp/CustomAllocator.cpp b/kotlin-native/runtime/src/custom_alloc/cpp/CustomAllocator.cpp
index 49e9a7e971f..a5dfedc0571 100644
--- a/kotlin-native/runtime/src/custom_alloc/cpp/CustomAllocator.cpp
+++ b/kotlin-native/runtime/src/custom_alloc/cpp/CustomAllocator.cpp
@@ -17,13 +17,12 @@
 #include "ExtraObjectData.hpp"
 #include "ExtraObjectPage.hpp"
 #include "GCScheduler.hpp"
-#include "LargePage.hpp"
-#include "MediumPage.hpp"
+#include "SingleObjectPage.hpp"
+#include "NextFitPage.hpp"
 #include "Memory.h"
-#include "SmallPage.hpp"
+#include "FixedBlockPage.hpp"
 #include "GCImpl.hpp"
 #include "TypeInfo.h"
-#include "Types.h"
 
 namespace kotlin::alloc {
 
@@ -55,9 +54,9 @@ uint64_t ArrayAllocatedDataSize(const TypeInfo* typeInfo, uint32_t count) noexce
 }
 
 CustomAllocator::CustomAllocator(Heap& heap, gc::GCSchedulerThreadData& gcScheduler) noexcept :
-    heap_(heap), gcScheduler_(gcScheduler), mediumPage_(nullptr), extraObjectPage_(nullptr) {
+    heap_(heap), gcScheduler_(gcScheduler), nextFitPage_(nullptr), extraObjectPage_(nullptr) {
     CustomAllocInfo("CustomAllocator::CustomAllocator(heap)");
-    memset(smallPages_, 0, sizeof(smallPages_));
+    memset(fixedBlockPages_, 0, sizeof(fixedBlockPages_));
 }
 
 ObjHeader* CustomAllocator::CreateObject(const TypeInfo* typeInfo) noexcept {
@@ -115,8 +114,8 @@ mm::ExtraObjectData& CustomAllocator::CreateExtraObjectDataForObject(
 
 void CustomAllocator::PrepareForGC() noexcept {
     CustomAllocInfo("CustomAllocator@%p::PrepareForGC()", this);
-    mediumPage_ = nullptr;
-    memset(smallPages_, 0, sizeof(smallPages_));
+    nextFitPage_ = nullptr;
+    memset(fixedBlockPages_, 0, sizeof(fixedBlockPages_));
     extraObjectPage_ = nullptr;
 }
 
@@ -125,49 +124,49 @@ uint8_t* CustomAllocator::Allocate(uint64_t size) noexcept {
     CustomAllocDebug("CustomAllocator::Allocate(%" PRIu64 ")", size);
     uint64_t cellCount = (size + sizeof(Cell) - 1) / sizeof(Cell);
     uint8_t* ptr;
-    if (cellCount <= SMALL_PAGE_MAX_BLOCK_SIZE) {
-        ptr = AllocateInSmallPage(cellCount);
-    } else if (cellCount > MEDIUM_PAGE_MAX_BLOCK_SIZE) {
-        ptr = AllocateInLargePage(cellCount);
+    if (cellCount <= FIXED_BLOCK_PAGE_MAX_BLOCK_SIZE) {
+        ptr = AllocateInFixedBlockPage(cellCount);
+    } else if (cellCount > NEXT_FIT_PAGE_MAX_BLOCK_SIZE) {
+        ptr = AllocateInSingleObjectPage(cellCount);
     } else {
-        ptr = AllocateInMediumPage(cellCount);
+        ptr = AllocateInNextFitPage(cellCount);
     }
     memset(ptr, 0, size);
     return ptr;
 }
 
-uint8_t* CustomAllocator::AllocateInLargePage(uint64_t cellCount) noexcept {
-    CustomAllocDebug("CustomAllocator::AllocateInLargePage(%" PRIu64 ")", cellCount);
-    uint8_t* block = heap_.GetLargePage(cellCount)->TryAllocate();
+uint8_t* CustomAllocator::AllocateInSingleObjectPage(uint64_t cellCount) noexcept {
+    CustomAllocDebug("CustomAllocator::AllocateInSingleObjectPage(%" PRIu64 ")", cellCount);
+    uint8_t* block = heap_.GetSingleObjectPage(cellCount)->TryAllocate();
     return block;
 }
 
-uint8_t* CustomAllocator::AllocateInMediumPage(uint32_t cellCount) noexcept {
-    CustomAllocDebug("CustomAllocator::AllocateInMediumPage(%u)", cellCount);
-    if (mediumPage_) {
-        uint8_t* block = mediumPage_->TryAllocate(cellCount);
+uint8_t* CustomAllocator::AllocateInNextFitPage(uint32_t cellCount) noexcept {
+    CustomAllocDebug("CustomAllocator::AllocateInNextFitPage(%u)", cellCount);
+    if (nextFitPage_) {
+        uint8_t* block = nextFitPage_->TryAllocate(cellCount);
         if (block) return block;
     }
     CustomAllocDebug("Failed to allocate in curPage");
     while (true) {
-        mediumPage_ = heap_.GetMediumPage(cellCount);
-        uint8_t* block = mediumPage_->TryAllocate(cellCount);
+        nextFitPage_ = heap_.GetNextFitPage(cellCount);
+        uint8_t* block = nextFitPage_->TryAllocate(cellCount);
         if (block) return block;
     }
 }
 
-uint8_t* CustomAllocator::AllocateInSmallPage(uint32_t cellCount) noexcept {
-    CustomAllocDebug("CustomAllocator::AllocateInSmallPage(%u)", cellCount);
-    SmallPage* page = smallPages_[cellCount];
+uint8_t* CustomAllocator::AllocateInFixedBlockPage(uint32_t cellCount) noexcept {
+    CustomAllocDebug("CustomAllocator::AllocateInFixedBlockPage(%u)", cellCount);
+    FixedBlockPage* page = fixedBlockPages_[cellCount];
     if (page) {
         uint8_t* block = page->TryAllocate();
         if (block) return block;
     }
-    CustomAllocDebug("Failed to allocate in current SmallPage");
-    while ((page = heap_.GetSmallPage(cellCount))) {
+    CustomAllocDebug("Failed to allocate in current FixedBlockPage");
+    while ((page = heap_.GetFixedBlockPage(cellCount))) {
         uint8_t* block = page->TryAllocate();
         if (block) {
-            smallPages_[cellCount] = page;
+            fixedBlockPages_[cellCount] = page;
             return block;
         }
     }
diff --git a/kotlin-native/runtime/src/custom_alloc/cpp/CustomAllocator.hpp b/kotlin-native/runtime/src/custom_alloc/cpp/CustomAllocator.hpp
index d9f74e46b14..5b058ca013a 100644
--- a/kotlin-native/runtime/src/custom_alloc/cpp/CustomAllocator.hpp
+++ b/kotlin-native/runtime/src/custom_alloc/cpp/CustomAllocator.hpp
@@ -13,9 +13,9 @@
 #include "ExtraObjectPage.hpp"
 #include "GCScheduler.hpp"
 #include "Heap.hpp"
-#include "MediumPage.hpp"
+#include "NextFitPage.hpp"
 #include "Memory.h"
-#include "SmallPage.hpp"
+#include "FixedBlockPage.hpp"
 
 namespace kotlin::alloc {
 
@@ -36,14 +36,14 @@ public:
 
 private:
     uint8_t* Allocate(uint64_t cellCount) noexcept;
-    uint8_t* AllocateInLargePage(uint64_t cellCount) noexcept;
-    uint8_t* AllocateInMediumPage(uint32_t cellCount) noexcept;
-    uint8_t* AllocateInSmallPage(uint32_t cellCount) noexcept;
+    uint8_t* AllocateInSingleObjectPage(uint64_t cellCount) noexcept;
+    uint8_t* AllocateInNextFitPage(uint32_t cellCount) noexcept;
+    uint8_t* AllocateInFixedBlockPage(uint32_t cellCount) noexcept;
 
     Heap& heap_;
     gc::GCSchedulerThreadData& gcScheduler_;
-    MediumPage* mediumPage_;
-    SmallPage* smallPages_[SMALL_PAGE_MAX_BLOCK_SIZE + 1];
+    NextFitPage* nextFitPage_;
+    FixedBlockPage* fixedBlockPages_[FIXED_BLOCK_PAGE_MAX_BLOCK_SIZE + 1];
     ExtraObjectPage* extraObjectPage_;
 };
 
diff --git a/kotlin-native/runtime/src/custom_alloc/cpp/CustomAllocatorTest.cpp b/kotlin-native/runtime/src/custom_alloc/cpp/CustomAllocatorTest.cpp
index 48378da66c2..c9e402e0996 100644
--- a/kotlin-native/runtime/src/custom_alloc/cpp/CustomAllocatorTest.cpp
+++ b/kotlin-native/runtime/src/custom_alloc/cpp/CustomAllocatorTest.cpp
@@ -39,9 +39,9 @@ TEST(CustomAllocTest, SmallAllocNonNull) {
     }
 }
 
-TEST(CustomAllocTest, SmallAllocSameSmallPage) {
-    const int N = SMALL_PAGE_CELL_COUNT / SMALL_PAGE_MAX_BLOCK_SIZE;
-    for (int blocks = MIN_BLOCK_SIZE; blocks < SMALL_PAGE_MAX_BLOCK_SIZE; ++blocks) {
+TEST(CustomAllocTest, SmallAllocSameFixedBlockPage) {
+    const int N = FIXED_BLOCK_PAGE_CELL_COUNT / FIXED_BLOCK_PAGE_MAX_BLOCK_SIZE;
+    for (int blocks = MIN_BLOCK_SIZE; blocks < FIXED_BLOCK_PAGE_MAX_BLOCK_SIZE; ++blocks) {
         Heap heap;
         kotlin::gc::GCSchedulerConfig config;
         kotlin::gc::GCSchedulerThreadData schedulerData(config, [](auto&) {});
@@ -51,31 +51,31 @@ TEST(CustomAllocTest, SmallAllocSameSmallPage) {
         for (int i = 1; i < N; ++i) {
             uint8_t* obj = reinterpret_cast<uint8_t*>(ca.CreateObject(&fakeType));
             uint64_t dist = abs(obj - first);
-            EXPECT_TRUE(dist < SMALL_PAGE_SIZE);
+            EXPECT_TRUE(dist < FIXED_BLOCK_PAGE_SIZE);
         }
     }
 }
 
-TEST(CustomAllocTest, SmallPageThreshold) {
+TEST(CustomAllocTest, FixedBlockPageThreshold) {
     Heap heap;
     kotlin::gc::GCSchedulerConfig config;
     kotlin::gc::GCSchedulerThreadData schedulerData(config, [](auto&) {});
     CustomAllocator ca(heap, schedulerData);
-    const int FROM = SMALL_PAGE_MAX_BLOCK_SIZE - 10;
-    const int TO = SMALL_PAGE_MAX_BLOCK_SIZE + 10;
+    const int FROM = FIXED_BLOCK_PAGE_MAX_BLOCK_SIZE - 10;
+    const int TO = FIXED_BLOCK_PAGE_MAX_BLOCK_SIZE + 10;
     for (int blocks = FROM; blocks <= TO; ++blocks) {
         TypeInfo fakeType = {.instanceSize_ = 8 * blocks, .flags_ = 0};
         ca.CreateObject(&fakeType);
     }
 }
 
-TEST(CustomAllocTest, MediumPageThreshold) {
+TEST(CustomAllocTest, NextFitPageThreshold) {
     Heap heap;
     kotlin::gc::GCSchedulerConfig config;
     kotlin::gc::GCSchedulerThreadData schedulerData(config, [](auto&) {});
     CustomAllocator ca(heap, schedulerData);
-    const int FROM = MEDIUM_PAGE_MAX_BLOCK_SIZE - 10;
-    const int TO = MEDIUM_PAGE_MAX_BLOCK_SIZE + 10;
+    const int FROM = NEXT_FIT_PAGE_MAX_BLOCK_SIZE - 10;
+    const int TO = NEXT_FIT_PAGE_MAX_BLOCK_SIZE + 10;
     for (int blocks = FROM; blocks <= TO; ++blocks) {
         TypeInfo fakeType = {.instanceSize_ = 8 * blocks, .flags_ = 0};
         ca.CreateObject(&fakeType);
@@ -94,7 +94,7 @@ TEST(CustomAllocTest, TwoAllocatorsDifferentPages) {
         uint8_t* obj1 = reinterpret_cast<uint8_t*>(ca1.CreateObject(&fakeType));
         uint8_t* obj2 = reinterpret_cast<uint8_t*>(ca2.CreateObject(&fakeType));
         uint64_t dist = abs(obj2 - obj1);
-        EXPECT_TRUE(dist >= SMALL_PAGE_SIZE);
+        EXPECT_TRUE(dist >= FIXED_BLOCK_PAGE_SIZE);
     }
 }
 
diff --git a/kotlin-native/runtime/src/custom_alloc/cpp/ExtraObjectPageTest.cpp b/kotlin-native/runtime/src/custom_alloc/cpp/ExtraObjectPageTest.cpp
index 4f8208838ff..6e0fb16a5d5 100644
--- a/kotlin-native/runtime/src/custom_alloc/cpp/ExtraObjectPageTest.cpp
+++ b/kotlin-native/runtime/src/custom_alloc/cpp/ExtraObjectPageTest.cpp
@@ -11,7 +11,6 @@
 #include "ExtraObjectData.hpp"
 #include "ExtraObjectPage.hpp"
 #include "gtest/gtest.h"
-#include "TypeInfo.h"
 
 namespace {
 
diff --git a/kotlin-native/runtime/src/custom_alloc/cpp/FixedBlockPage.cpp b/kotlin-native/runtime/src/custom_alloc/cpp/FixedBlockPage.cpp
new file mode 100644
index 00000000000..2fae4a792a5
--- /dev/null
+++ b/kotlin-native/runtime/src/custom_alloc/cpp/FixedBlockPage.cpp
@@ -0,0 +1,76 @@
+/*
+ * Copyright 2022 JetBrains s.r.o. Use of this source code is governed by the Apache 2.0 license
+ * that can be found in the LICENSE file.
+ */
+
+#include "FixedBlockPage.hpp"
+
+#include <atomic>
+#include <cstdint>
+#include <cstring>
+#include <random>
+
+#include "CustomLogging.hpp"
+#include "CustomAllocConstants.hpp"
+#include "GCApi.hpp"
+
+namespace kotlin::alloc {
+
+FixedBlockPage* FixedBlockPage::Create(uint32_t blockSize) noexcept {
+    CustomAllocInfo("FixedBlockPage::Create(%u)", blockSize);
+    RuntimeAssert(blockSize <= FIXED_BLOCK_PAGE_MAX_BLOCK_SIZE, "blockSize too large for FixedBlockPage");
+    return new (SafeAlloc(FIXED_BLOCK_PAGE_SIZE)) FixedBlockPage(blockSize);
+}
+
+void FixedBlockPage::Destroy() noexcept {
+    std_support::free(this);
+}
+
+FixedBlockPage::FixedBlockPage(uint32_t blockSize) noexcept : blockSize_(blockSize) {
+    CustomAllocInfo("FixedBlockPage(%p)::FixedBlockPage(%u)", this, blockSize);
+    nextFree_ = cells_;
+    FixedBlockCell* end = cells_ + (FIXED_BLOCK_PAGE_CELL_COUNT + 1 - blockSize_);
+    for (FixedBlockCell* cell = cells_; cell < end; cell = cell->nextFree) {
+        cell->nextFree = cell + blockSize;
+    }
+}
+
+uint8_t* FixedBlockPage::TryAllocate() noexcept {
+    FixedBlockCell* end = cells_ + (FIXED_BLOCK_PAGE_CELL_COUNT + 1 - blockSize_);
+    FixedBlockCell* freeBlock = nextFree_;
+    if (freeBlock >= end) {
+        return nullptr;
+    }
+    nextFree_ = freeBlock->nextFree;
+    CustomAllocDebug("FixedBlockPage(%p){%u}::TryAllocate() = %p", this, blockSize_, freeBlock);
+    return freeBlock->data;
+}
+
+bool FixedBlockPage::Sweep() noexcept {
+    CustomAllocInfo("FixedBlockPage(%p)::Sweep()", this);
+    // `end` is after the last legal allocation of a block, but does not
+    // necessarily match an actual block starting point.
+    FixedBlockCell* end = cells_ + (FIXED_BLOCK_PAGE_CELL_COUNT + 1 - blockSize_);
+    bool alive = false;
+    FixedBlockCell** nextFree = &nextFree_;
+    for (FixedBlockCell* cell = cells_; cell < end; cell += blockSize_) {
+        // If the current cell is free, move on.
+        if (cell == *nextFree) {
+            nextFree = &cell->nextFree;
+            continue;
+        }
+        // If the current cell was marked, it's alive, and the whole page is alive.
+        if (TryResetMark(cell)) {
+            alive = true;
+            continue;
+        }
+        CustomAllocInfo("FixedBlockPage(%p)::Sweep: reclaim %p", this, cell);
+        // Free the current block and insert it into the free list.
+        cell->nextFree = *nextFree;
+        *nextFree = cell;
+        nextFree = &cell->nextFree;
+    }
+    return alive;
+}
+
+} // namespace kotlin::alloc
diff --git a/kotlin-native/runtime/src/custom_alloc/cpp/SmallPage.hpp b/kotlin-native/runtime/src/custom_alloc/cpp/FixedBlockPage.hpp
similarity index 54%
rename from kotlin-native/runtime/src/custom_alloc/cpp/SmallPage.hpp
rename to kotlin-native/runtime/src/custom_alloc/cpp/FixedBlockPage.hpp
index c33c6dab300..95a0b532f0d 100644
--- a/kotlin-native/runtime/src/custom_alloc/cpp/SmallPage.hpp
+++ b/kotlin-native/runtime/src/custom_alloc/cpp/FixedBlockPage.hpp
@@ -3,8 +3,8 @@
  * that can be found in the LICENSE file.
  */
 
-#ifndef CUSTOM_ALLOC_CPP_SMALLPAGE_HPP_
-#define CUSTOM_ALLOC_CPP_SMALLPAGE_HPP_
+#ifndef CUSTOM_ALLOC_CPP_FIXEDBLOCKPAGE_HPP_
+#define CUSTOM_ALLOC_CPP_FIXEDBLOCKPAGE_HPP_
 
 #include <atomic>
 #include <cstdint>
@@ -13,17 +13,17 @@
 
 namespace kotlin::alloc {
 
-struct alignas(8) SmallCell {
-    // The SmallCell either contains data or a pointer to the next free cell
+struct alignas(8) FixedBlockCell {
+    // The FixedBlockCell either contains data or a pointer to the next free cell
     union {
         uint8_t data[];
-        SmallCell* nextFree;
+        FixedBlockCell* nextFree;
     };
 };
 
-class alignas(8) SmallPage {
+class alignas(8) FixedBlockPage {
 public:
-    static SmallPage* Create(uint32_t blockSize) noexcept;
+    static FixedBlockPage* Create(uint32_t blockSize) noexcept;
 
     void Destroy() noexcept;
 
@@ -33,15 +33,15 @@ public:
     bool Sweep() noexcept;
 
 private:
-    friend class AtomicStack<SmallPage>;
+    friend class AtomicStack<FixedBlockPage>;
 
-    explicit SmallPage(uint32_t blockSize) noexcept;
+    explicit FixedBlockPage(uint32_t blockSize) noexcept;
 
     // Used for linking pages together in `pages` queue or in `unswept` queue.
-    SmallPage* next_;
+    FixedBlockPage* next_;
     uint32_t blockSize_;
-    SmallCell* nextFree_;
-    SmallCell cells_[];
+    FixedBlockCell* nextFree_;
+    FixedBlockCell cells_[];
 };
 
 } // namespace kotlin::alloc
diff --git a/kotlin-native/runtime/src/custom_alloc/cpp/SmallPageTest.cpp b/kotlin-native/runtime/src/custom_alloc/cpp/FixedBlockPageTest.cpp
similarity index 54%
rename from kotlin-native/runtime/src/custom_alloc/cpp/SmallPageTest.cpp
rename to kotlin-native/runtime/src/custom_alloc/cpp/FixedBlockPageTest.cpp
index e2fbaddaf15..554d3ae1431 100644
--- a/kotlin-native/runtime/src/custom_alloc/cpp/SmallPageTest.cpp
+++ b/kotlin-native/runtime/src/custom_alloc/cpp/FixedBlockPageTest.cpp
@@ -8,12 +8,12 @@
 #include "Cell.hpp"
 #include "CustomAllocConstants.hpp"
 #include "gtest/gtest.h"
-#include "SmallPage.hpp"
+#include "FixedBlockPage.hpp"
 #include "TypeInfo.h"
 
 namespace {
 
-using SmallPage = typename kotlin::alloc::SmallPage;
+using FixedBlockPage = typename kotlin::alloc::FixedBlockPage;
 
 TypeInfo fakeType = {.flags_ = 0}; // a type without a finalizer
 
@@ -21,7 +21,7 @@ void mark(void* obj) {
     reinterpret_cast<uint64_t*>(obj)[0] = 1;
 }
 
-uint8_t* alloc(SmallPage* page, size_t blockSize) {
+uint8_t* alloc(FixedBlockPage* page, size_t blockSize) {
     uint8_t* ptr = page->TryAllocate();
     if (ptr) {
         memset(ptr, 0, 8 * blockSize);
@@ -30,9 +30,9 @@ uint8_t* alloc(SmallPage* page, size_t blockSize) {
     return ptr;
 }
 
-TEST(CustomAllocTest, SmallPageConsequtiveAlloc) {
-    for (uint32_t size = 2; size <= SMALL_PAGE_MAX_BLOCK_SIZE; ++size) {
-        SmallPage* page = SmallPage::Create(size);
+TEST(CustomAllocTest, FixedBlockPageConsequtiveAlloc) {
+    for (uint32_t size = 2; size <= FIXED_BLOCK_PAGE_MAX_BLOCK_SIZE; ++size) {
+        FixedBlockPage* page = FixedBlockPage::Create(size);
         uint8_t* prev = alloc(page, size);
         uint8_t* cur;
         while ((cur = alloc(page, size))) {
@@ -43,28 +43,28 @@ TEST(CustomAllocTest, SmallPageConsequtiveAlloc) {
     }
 }
 
-TEST(CustomAllocTest, SmallPageSweepEmptyPage) {
-    for (uint32_t size = 2; size <= SMALL_PAGE_MAX_BLOCK_SIZE; ++size) {
-        SmallPage* page = SmallPage::Create(size);
+TEST(CustomAllocTest, FixedBlockPageSweepEmptyPage) {
+    for (uint32_t size = 2; size <= FIXED_BLOCK_PAGE_MAX_BLOCK_SIZE; ++size) {
+        FixedBlockPage* page = FixedBlockPage::Create(size);
         EXPECT_FALSE(page->Sweep());
         page->Destroy();
     }
 }
 
-TEST(CustomAllocTest, SmallPageSweepFullUnmarkedPage) {
-    for (uint32_t size = 2; size <= SMALL_PAGE_MAX_BLOCK_SIZE; ++size) {
-        SmallPage* page = SmallPage::Create(size);
+TEST(CustomAllocTest, FixedBlockPageSweepFullUnmarkedPage) {
+    for (uint32_t size = 2; size <= FIXED_BLOCK_PAGE_MAX_BLOCK_SIZE; ++size) {
+        FixedBlockPage* page = FixedBlockPage::Create(size);
         uint32_t count = 0;
         while (alloc(page, size)) ++count;
-        EXPECT_EQ(count, SMALL_PAGE_CELL_COUNT / size);
+        EXPECT_EQ(count, FIXED_BLOCK_PAGE_CELL_COUNT / size);
         EXPECT_FALSE(page->Sweep());
         page->Destroy();
     }
 }
 
-TEST(CustomAllocTest, SmallPageSweepSingleMarked) {
-    for (uint32_t size = 2; size <= SMALL_PAGE_MAX_BLOCK_SIZE; ++size) {
-        SmallPage* page = SmallPage::Create(size);
+TEST(CustomAllocTest, FixedBlockPageSweepSingleMarked) {
+    for (uint32_t size = 2; size <= FIXED_BLOCK_PAGE_MAX_BLOCK_SIZE; ++size) {
+        FixedBlockPage* page = FixedBlockPage::Create(size);
         uint8_t* ptr = alloc(page, size);
         mark(ptr);
         EXPECT_TRUE(page->Sweep());
@@ -72,9 +72,9 @@ TEST(CustomAllocTest, SmallPageSweepSingleMarked) {
     }
 }
 
-TEST(CustomAllocTest, SmallPageSweepSingleReuse) {
-    for (uint32_t size = 2; size <= SMALL_PAGE_MAX_BLOCK_SIZE; ++size) {
-        SmallPage* page = SmallPage::Create(size);
+TEST(CustomAllocTest, FixedBlockPageSweepSingleReuse) {
+    for (uint32_t size = 2; size <= FIXED_BLOCK_PAGE_MAX_BLOCK_SIZE; ++size) {
+        FixedBlockPage* page = FixedBlockPage::Create(size);
         uint8_t* ptr = alloc(page, size);
         EXPECT_FALSE(page->Sweep());
         EXPECT_EQ(alloc(page, size), ptr);
@@ -82,9 +82,9 @@ TEST(CustomAllocTest, SmallPageSweepSingleReuse) {
     }
 }
 
-TEST(CustomAllocTest, SmallPageSweepReuse) {
-    for (uint32_t size = 2; size <= SMALL_PAGE_MAX_BLOCK_SIZE; ++size) {
-        SmallPage* page = SmallPage::Create(size);
+TEST(CustomAllocTest, FixedBlockPageSweepReuse) {
+    for (uint32_t size = 2; size <= FIXED_BLOCK_PAGE_MAX_BLOCK_SIZE; ++size) {
+        FixedBlockPage* page = FixedBlockPage::Create(size);
         uint8_t* ptr;
         for (int count = 0; (ptr = alloc(page, size)); ++count) {
             if (count % 2 == 0) mark(ptr);
@@ -94,7 +94,7 @@ TEST(CustomAllocTest, SmallPageSweepReuse) {
         for (; (ptr = alloc(page, size)); ++count) {
             if (count % 2 == 0) mark(ptr);
         }
-        EXPECT_EQ(count, SMALL_PAGE_CELL_COUNT / size / 2);
+        EXPECT_EQ(count, FIXED_BLOCK_PAGE_CELL_COUNT / size / 2);
         page->Destroy();
     }
 }
diff --git a/kotlin-native/runtime/src/custom_alloc/cpp/Heap.cpp b/kotlin-native/runtime/src/custom_alloc/cpp/Heap.cpp
index aab0c7646f8..2a9075e0fa7 100644
--- a/kotlin-native/runtime/src/custom_alloc/cpp/Heap.cpp
+++ b/kotlin-native/runtime/src/custom_alloc/cpp/Heap.cpp
@@ -32,21 +32,21 @@ void Heap::PrepareForGC() noexcept {
         thread.gc().impl().alloc().PrepareForGC();
     }
 
-    mediumPages_.PrepareForGC();
-    largePages_.PrepareForGC();
-    for (int blockSize = 0; blockSize <= SMALL_PAGE_MAX_BLOCK_SIZE; ++blockSize) {
-        smallPages_[blockSize].PrepareForGC();
+    nextFitPages_.PrepareForGC();
+    singleObjectPages_.PrepareForGC();
+    for (int blockSize = 0; blockSize <= FIXED_BLOCK_PAGE_MAX_BLOCK_SIZE; ++blockSize) {
+        fixedBlockPages_[blockSize].PrepareForGC();
     }
     usedExtraObjectPages_.TransferAllFrom(std::move(extraObjectPages_));
 }
 
 void Heap::Sweep() noexcept {
     CustomAllocDebug("Heap::Sweep()");
-    for (int blockSize = 0; blockSize <= SMALL_PAGE_MAX_BLOCK_SIZE; ++blockSize) {
-        smallPages_[blockSize].Sweep();
+    for (int blockSize = 0; blockSize <= FIXED_BLOCK_PAGE_MAX_BLOCK_SIZE; ++blockSize) {
+        fixedBlockPages_[blockSize].Sweep();
     }
-    mediumPages_.Sweep();
-    largePages_.SweepAndFree();
+    nextFitPages_.Sweep();
+    singleObjectPages_.SweepAndFree();
 }
 
 AtomicStack<ExtraObjectCell> Heap::SweepExtraObjects(gc::GCHandle gcHandle) noexcept {
@@ -64,19 +64,19 @@ AtomicStack<ExtraObjectCell> Heap::SweepExtraObjects(gc::GCHandle gcHandle) noex
     return finalizerQueue;
 }
 
-MediumPage* Heap::GetMediumPage(uint32_t cellCount) noexcept {
-    CustomAllocDebug("Heap::GetMediumPage()");
-    return mediumPages_.GetPage(cellCount);
+NextFitPage* Heap::GetNextFitPage(uint32_t cellCount) noexcept {
+    CustomAllocDebug("Heap::GetNextFitPage()");
+    return nextFitPages_.GetPage(cellCount);
 }
 
-SmallPage* Heap::GetSmallPage(uint32_t cellCount) noexcept {
-    CustomAllocDebug("Heap::GetSmallPage()");
-    return smallPages_[cellCount].GetPage(cellCount);
+FixedBlockPage* Heap::GetFixedBlockPage(uint32_t cellCount) noexcept {
+    CustomAllocDebug("Heap::GetFixedBlockPage()");
+    return fixedBlockPages_[cellCount].GetPage(cellCount);
 }
 
-LargePage* Heap::GetLargePage(uint64_t cellCount) noexcept {
-    CustomAllocInfo("CustomAllocator::AllocateInLargePage(%" PRIu64 ")", cellCount);
-    return largePages_.NewPage(cellCount);
+SingleObjectPage* Heap::GetSingleObjectPage(uint64_t cellCount) noexcept {
+    CustomAllocInfo("CustomAllocator::AllocateInSingleObjectPage(%" PRIu64 ")", cellCount);
+    return singleObjectPages_.NewPage(cellCount);
 }
 
 ExtraObjectPage* Heap::GetExtraObjectPage() noexcept {
diff --git a/kotlin-native/runtime/src/custom_alloc/cpp/Heap.hpp b/kotlin-native/runtime/src/custom_alloc/cpp/Heap.hpp
index 0840dcb6a1b..0325a0ad34c 100644
--- a/kotlin-native/runtime/src/custom_alloc/cpp/Heap.hpp
+++ b/kotlin-native/runtime/src/custom_alloc/cpp/Heap.hpp
@@ -13,10 +13,10 @@
 #include "CustomAllocConstants.hpp"
 #include "ExtraObjectPage.hpp"
 #include "GCStatistics.hpp"
-#include "LargePage.hpp"
-#include "MediumPage.hpp"
+#include "SingleObjectPage.hpp"
+#include "NextFitPage.hpp"
 #include "PageStore.hpp"
-#include "SmallPage.hpp"
+#include "FixedBlockPage.hpp"
 
 namespace kotlin::alloc {
 
@@ -34,15 +34,15 @@ public:
 
     AtomicStack<ExtraObjectCell> SweepExtraObjects(gc::GCHandle gcHandle) noexcept;
 
-    SmallPage* GetSmallPage(uint32_t cellCount) noexcept;
-    MediumPage* GetMediumPage(uint32_t cellCount) noexcept;
-    LargePage* GetLargePage(uint64_t cellCount) noexcept;
+    FixedBlockPage* GetFixedBlockPage(uint32_t cellCount) noexcept;
+    NextFitPage* GetNextFitPage(uint32_t cellCount) noexcept;
+    SingleObjectPage* GetSingleObjectPage(uint64_t cellCount) noexcept;
     ExtraObjectPage* GetExtraObjectPage() noexcept;
 
 private:
-    PageStore<SmallPage> smallPages_[SMALL_PAGE_MAX_BLOCK_SIZE + 1];
-    PageStore<MediumPage> mediumPages_;
-    PageStore<LargePage> largePages_;
+    PageStore<FixedBlockPage> fixedBlockPages_[FIXED_BLOCK_PAGE_MAX_BLOCK_SIZE + 1];
+    PageStore<NextFitPage> nextFitPages_;
+    PageStore<SingleObjectPage> singleObjectPages_;
     AtomicStack<ExtraObjectPage> extraObjectPages_;
     AtomicStack<ExtraObjectPage> usedExtraObjectPages_;
 };
diff --git a/kotlin-native/runtime/src/custom_alloc/cpp/HeapTest.cpp b/kotlin-native/runtime/src/custom_alloc/cpp/HeapTest.cpp
index 25f45e4dd8d..9ed2e6e2502 100644
--- a/kotlin-native/runtime/src/custom_alloc/cpp/HeapTest.cpp
+++ b/kotlin-native/runtime/src/custom_alloc/cpp/HeapTest.cpp
@@ -7,17 +7,17 @@
 #include <cstdint>
 #include <random>
 
-#include "LargePage.hpp"
+#include "SingleObjectPage.hpp"
 #include "gtest/gtest.h"
 #include "Heap.hpp"
-#include "SmallPage.hpp"
+#include "FixedBlockPage.hpp"
 
 namespace {
 
 using Heap = typename kotlin::alloc::Heap;
-using SmallPage = typename kotlin::alloc::SmallPage;
-using MediumPage = typename kotlin::alloc::MediumPage;
-using LargePage = typename kotlin::alloc::LargePage;
+using FixedBlockPage = typename kotlin::alloc::FixedBlockPage;
+using NextFitPage = typename kotlin::alloc::NextFitPage;
+using SingleObjectPage = typename kotlin::alloc::SingleObjectPage;
 
 inline constexpr int MIN_BLOCK_SIZE = 2;
 
@@ -25,32 +25,32 @@ void mark(void* obj) {
     reinterpret_cast<uint64_t*>(obj)[0] = 1;
 }
 
-TEST(CustomAllocTest, HeapReuseSmallPages) {
+TEST(CustomAllocTest, HeapReuseFixedBlockPages) {
     Heap heap;
     const int MIN = MIN_BLOCK_SIZE;
-    const int MAX = SMALL_PAGE_MAX_BLOCK_SIZE + 1;
-    SmallPage* pages[MAX];
+    const int MAX = FIXED_BLOCK_PAGE_MAX_BLOCK_SIZE + 1;
+    FixedBlockPage* pages[MAX];
     for (int blocks = MIN; blocks < MAX; ++blocks) {
-        pages[blocks] = heap.GetSmallPage(blocks);
+        pages[blocks] = heap.GetFixedBlockPage(blocks);
         void* obj = pages[blocks]->TryAllocate();
         mark(obj); // to make the page survive a sweep
     }
     heap.PrepareForGC();
     heap.Sweep();
     for (int blocks = MIN; blocks < MAX; ++blocks) {
-        EXPECT_EQ(pages[blocks], heap.GetSmallPage(blocks));
+        EXPECT_EQ(pages[blocks], heap.GetFixedBlockPage(blocks));
     }
 }
 
-TEST(CustomAllocTest, HeapReuseMediumPages) {
+TEST(CustomAllocTest, HeapReuseNextFitPages) {
     Heap heap;
-    const uint32_t BLOCKSIZE = SMALL_PAGE_MAX_BLOCK_SIZE + 42;
-    MediumPage* page = heap.GetMediumPage(BLOCKSIZE);
+    const uint32_t BLOCKSIZE = FIXED_BLOCK_PAGE_MAX_BLOCK_SIZE + 42;
+    NextFitPage* page = heap.GetNextFitPage(BLOCKSIZE);
     void* obj = page->TryAllocate(BLOCKSIZE);
     mark(obj); // to make the page survive a sweep
     heap.PrepareForGC();
     heap.Sweep();
-    EXPECT_EQ(page, heap.GetMediumPage(BLOCKSIZE));
+    EXPECT_EQ(page, heap.GetNextFitPage(BLOCKSIZE));
 }
 
 } // namespace
diff --git a/kotlin-native/runtime/src/custom_alloc/cpp/LargePage.cpp b/kotlin-native/runtime/src/custom_alloc/cpp/LargePage.cpp
deleted file mode 100644
index 0b2943b81ff..00000000000
--- a/kotlin-native/runtime/src/custom_alloc/cpp/LargePage.cpp
+++ /dev/null
@@ -1,47 +0,0 @@
-/*
- * Copyright 2022 JetBrains s.r.o. Use of this source code is governed by the Apache 2.0 license
- * that can be found in the LICENSE file.
- */
-
-#include "LargePage.hpp"
-
-#include <atomic>
-#include <cstdint>
-
-#include "CustomLogging.hpp"
-#include "CustomAllocConstants.hpp"
-#include "GCApi.hpp"
-
-namespace kotlin::alloc {
-
-LargePage* LargePage::Create(uint64_t cellCount) noexcept {
-    CustomAllocInfo("LargePage::Create(%" PRIu64 ")", cellCount);
-    RuntimeAssert(cellCount > MEDIUM_PAGE_MAX_BLOCK_SIZE, "blockSize too small for large page");
-    uint64_t size = sizeof(LargePage) + cellCount * sizeof(uint64_t);
-    return new (SafeAlloc(size)) LargePage();
-}
-
-void LargePage::Destroy() noexcept {
-    std_support::free(this);
-}
-
-uint8_t* LargePage::Data() noexcept {
-    return data_;
-}
-
-uint8_t* LargePage::TryAllocate() noexcept {
-    if (isAllocated_) return nullptr;
-    isAllocated_ = true;
-    return Data();
-}
-
-bool LargePage::Sweep() noexcept {
-    CustomAllocDebug("LargePage@%p::Sweep()", this);
-    if (!TryResetMark(Data())) {
-        isAllocated_ = false;
-        return false;
-    }
-    return true;
-}
-
-} // namespace kotlin::alloc
diff --git a/kotlin-native/runtime/src/custom_alloc/cpp/MediumPage.cpp b/kotlin-native/runtime/src/custom_alloc/cpp/NextFitPage.cpp
similarity index 63%
rename from kotlin-native/runtime/src/custom_alloc/cpp/MediumPage.cpp
rename to kotlin-native/runtime/src/custom_alloc/cpp/NextFitPage.cpp
index 1b84f31e516..6ddb52384fe 100644
--- a/kotlin-native/runtime/src/custom_alloc/cpp/MediumPage.cpp
+++ b/kotlin-native/runtime/src/custom_alloc/cpp/NextFitPage.cpp
@@ -3,7 +3,7 @@
  * that can be found in the LICENSE file.
  */
 
-#include "MediumPage.hpp"
+#include "NextFitPage.hpp"
 
 #include <atomic>
 #include <cstdint>
@@ -14,23 +14,23 @@
 
 namespace kotlin::alloc {
 
-MediumPage* MediumPage::Create(uint32_t cellCount) noexcept {
-    CustomAllocInfo("MediumPage::Create(%u)", cellCount);
-    RuntimeAssert(cellCount < MEDIUM_PAGE_CELL_COUNT, "cellCount is too large for medium page");
-    return new (SafeAlloc(MEDIUM_PAGE_SIZE)) MediumPage(cellCount);
+NextFitPage* NextFitPage::Create(uint32_t cellCount) noexcept {
+    CustomAllocInfo("NextFitPage::Create(%u)", cellCount);
+    RuntimeAssert(cellCount < NEXT_FIT_PAGE_CELL_COUNT, "cellCount is too large for NextFitPage");
+    return new (SafeAlloc(NEXT_FIT_PAGE_SIZE)) NextFitPage(cellCount);
 }
 
-void MediumPage::Destroy() noexcept {
+void NextFitPage::Destroy() noexcept {
     std_support::free(this);
 }
 
-MediumPage::MediumPage(uint32_t cellCount) noexcept : curBlock_(cells_) {
+NextFitPage::NextFitPage(uint32_t cellCount) noexcept : curBlock_(cells_) {
     cells_[0] = Cell(0); // Size 0 ensures any actual use would break
-    cells_[1] = Cell(MEDIUM_PAGE_CELL_COUNT - 1);
+    cells_[1] = Cell(NEXT_FIT_PAGE_CELL_COUNT - 1);
 }
 
-uint8_t* MediumPage::TryAllocate(uint32_t blockSize) noexcept {
-    CustomAllocDebug("MediumPage@%p::TryAllocate(%u)", this, blockSize);
+uint8_t* NextFitPage::TryAllocate(uint32_t blockSize) noexcept {
+    CustomAllocDebug("NextFitPage@%p::TryAllocate(%u)", this, blockSize);
     // +1 accounts for header, since cell->size also includes header cell
     uint32_t cellsNeeded = blockSize + 1;
     uint8_t* block = curBlock_->TryAllocate(cellsNeeded);
@@ -39,9 +39,9 @@ uint8_t* MediumPage::TryAllocate(uint32_t blockSize) noexcept {
     return curBlock_->TryAllocate(cellsNeeded);
 }
 
-bool MediumPage::Sweep() noexcept {
-    CustomAllocDebug("MediumPage@%p::Sweep()", this);
-    Cell* end = cells_ + MEDIUM_PAGE_CELL_COUNT;
+bool NextFitPage::Sweep() noexcept {
+    CustomAllocDebug("NextFitPage@%p::Sweep()", this);
+    Cell* end = cells_ + NEXT_FIT_PAGE_CELL_COUNT;
     bool alive = false;
     for (Cell* block = cells_ + 1; block != end; block = block->Next()) {
         if (block->isAllocated_) {
@@ -64,10 +64,10 @@ bool MediumPage::Sweep() noexcept {
     return alive;
 }
 
-void MediumPage::UpdateCurBlock(uint32_t cellsNeeded) noexcept {
-    CustomAllocDebug("MediumPage@%p::UpdateCurBlock(%u)", this, cellsNeeded);
+void NextFitPage::UpdateCurBlock(uint32_t cellsNeeded) noexcept {
+    CustomAllocDebug("NextFitPage@%p::UpdateCurBlock(%u)", this, cellsNeeded);
     if (curBlock_ == cells_) curBlock_ = cells_ + 1; // only used as a starting point
-    Cell* end = cells_ + MEDIUM_PAGE_CELL_COUNT;
+    Cell* end = cells_ + NEXT_FIT_PAGE_CELL_COUNT;
     Cell* maxBlock = cells_; // size 0 block
     for (Cell* block = curBlock_; block != end; block = block->Next()) {
         if (!block->isAllocated_ && block->size_ > maxBlock->size_) {
@@ -78,7 +78,7 @@ void MediumPage::UpdateCurBlock(uint32_t cellsNeeded) noexcept {
             }
         }
     }
-    CustomAllocDebug("MediumPage@%p::UpdateCurBlock: starting from beginning", this);
+    CustomAllocDebug("NextFitPage@%p::UpdateCurBlock: starting from beginning", this);
     for (Cell* block = cells_ + 1; block != curBlock_; block = block->Next()) {
         if (!block->isAllocated_ && block->size_ > maxBlock->size_) {
             maxBlock = block;
@@ -91,12 +91,12 @@ void MediumPage::UpdateCurBlock(uint32_t cellsNeeded) noexcept {
     curBlock_ = maxBlock;
 }
 
-bool MediumPage::CheckInvariants() noexcept {
-    if (curBlock_ < cells_ || curBlock_ >= cells_ + MEDIUM_PAGE_CELL_COUNT) return false;
+bool NextFitPage::CheckInvariants() noexcept {
+    if (curBlock_ < cells_ || curBlock_ >= cells_ + NEXT_FIT_PAGE_CELL_COUNT) return false;
     for (Cell* cur = cells_ + 1;; cur = cur->Next()) {
         if (cur->Next() <= cur) return false;
-        if (cur->Next() > cells_ + MEDIUM_PAGE_CELL_COUNT) return false;
-        if (cur->Next() == cells_ + MEDIUM_PAGE_CELL_COUNT) return true;
+        if (cur->Next() > cells_ + NEXT_FIT_PAGE_CELL_COUNT) return false;
+        if (cur->Next() == cells_ + NEXT_FIT_PAGE_CELL_COUNT) return true;
     }
 }
 
diff --git a/kotlin-native/runtime/src/custom_alloc/cpp/MediumPage.hpp b/kotlin-native/runtime/src/custom_alloc/cpp/NextFitPage.hpp
similarity index 74%
rename from kotlin-native/runtime/src/custom_alloc/cpp/MediumPage.hpp
rename to kotlin-native/runtime/src/custom_alloc/cpp/NextFitPage.hpp
index 3908ad25746..b7a9563e60c 100644
--- a/kotlin-native/runtime/src/custom_alloc/cpp/MediumPage.hpp
+++ b/kotlin-native/runtime/src/custom_alloc/cpp/NextFitPage.hpp
@@ -3,8 +3,8 @@
  * that can be found in the LICENSE file.
  */
 
-#ifndef CUSTOM_ALLOC_CPP_MEDIUMPAGE_HPP_
-#define CUSTOM_ALLOC_CPP_MEDIUMPAGE_HPP_
+#ifndef CUSTOM_ALLOC_CPP_NEXTFITPAGE_HPP_
+#define CUSTOM_ALLOC_CPP_NEXTFITPAGE_HPP_
 
 #include <atomic>
 #include <cstdint>
@@ -14,9 +14,9 @@
 
 namespace kotlin::alloc {
 
-class alignas(8) MediumPage {
+class alignas(8) NextFitPage {
 public:
-    static MediumPage* Create(uint32_t cellCount) noexcept;
+    static NextFitPage* Create(uint32_t cellCount) noexcept;
 
     void Destroy() noexcept;
 
@@ -29,14 +29,14 @@ public:
     bool CheckInvariants() noexcept;
 
 private:
-    MediumPage(uint32_t cellCount) noexcept;
+    NextFitPage(uint32_t cellCount) noexcept;
 
     // Looks for a block big enough to hold cellsNeeded. If none big enough is
     // found, update to the largest one.
     void UpdateCurBlock(uint32_t cellsNeeded) noexcept;
 
-    friend class AtomicStack<MediumPage>;
-    MediumPage* next_;
+    friend class AtomicStack<NextFitPage>;
+    NextFitPage* next_;
 
     Cell* curBlock_;
     Cell cells_[]; // cells_[0] is reserved for an empty block
diff --git a/kotlin-native/runtime/src/custom_alloc/cpp/MediumPageTest.cpp b/kotlin-native/runtime/src/custom_alloc/cpp/NextFitPageTest.cpp
similarity index 68%
rename from kotlin-native/runtime/src/custom_alloc/cpp/MediumPageTest.cpp
rename to kotlin-native/runtime/src/custom_alloc/cpp/NextFitPageTest.cpp
index 886be8f1c96..1bb8306b770 100644
--- a/kotlin-native/runtime/src/custom_alloc/cpp/MediumPageTest.cpp
+++ b/kotlin-native/runtime/src/custom_alloc/cpp/NextFitPageTest.cpp
@@ -9,23 +9,23 @@
 #include "Cell.hpp"
 #include "CustomAllocConstants.hpp"
 #include "gtest/gtest.h"
-#include "MediumPage.hpp"
+#include "NextFitPage.hpp"
 #include "TypeInfo.h"
 
 namespace {
 
-using MediumPage = typename kotlin::alloc::MediumPage;
+using NextFitPage = typename kotlin::alloc::NextFitPage;
 using Cell = typename kotlin::alloc::Cell;
 
 TypeInfo fakeType = {.flags_ = 0}; // a type without a finalizer
 
-inline constexpr const size_t MIN_BLOCK_SIZE = SMALL_PAGE_MAX_BLOCK_SIZE + 1;
+inline constexpr const size_t MIN_BLOCK_SIZE = FIXED_BLOCK_PAGE_MAX_BLOCK_SIZE + 1;
 
 void mark(void* obj) {
     reinterpret_cast<uint64_t*>(obj)[0] = 1;
 }
 
-uint8_t* alloc(MediumPage* page, uint32_t blockSize) {
+uint8_t* alloc(NextFitPage* page, uint32_t blockSize) {
     uint8_t* ptr = page->TryAllocate(blockSize);
     if (!page->CheckInvariants()) {
         ADD_FAILURE();
@@ -41,8 +41,8 @@ uint8_t* alloc(MediumPage* page, uint32_t blockSize) {
     return ptr;
 }
 
-TEST(CustomAllocTest, MediumPageAlloc) {
-    MediumPage* page = MediumPage::Create(MIN_BLOCK_SIZE);
+TEST(CustomAllocTest, NextFitPageAlloc) {
+    NextFitPage* page = NextFitPage::Create(MIN_BLOCK_SIZE);
     uint8_t* p1 = alloc(page, MIN_BLOCK_SIZE);
     uint8_t* p2 = alloc(page, MIN_BLOCK_SIZE);
     uint64_t dist = abs(p1 - p2);
@@ -50,33 +50,33 @@ TEST(CustomAllocTest, MediumPageAlloc) {
     page->Destroy();
 }
 
-TEST(CustomAllocTest, MediumPageSweepEmptyPage) {
-    MediumPage* page = MediumPage::Create(MIN_BLOCK_SIZE);
+TEST(CustomAllocTest, NextFitPageSweepEmptyPage) {
+    NextFitPage* page = NextFitPage::Create(MIN_BLOCK_SIZE);
     EXPECT_FALSE(page->Sweep());
     page->Destroy();
 }
 
-TEST(CustomAllocTest, MediumPageSweepFullUnmarkedPage) {
+TEST(CustomAllocTest, NextFitPageSweepFullUnmarkedPage) {
     for (uint32_t seed = 0xC0FFEE0; seed <= 0xC0FFEEF; ++seed) {
         std::minstd_rand r(seed);
-        MediumPage* page = MediumPage::Create(MIN_BLOCK_SIZE);
+        NextFitPage* page = NextFitPage::Create(MIN_BLOCK_SIZE);
         while (alloc(page, MIN_BLOCK_SIZE + r() % 100)) {}
         EXPECT_FALSE(page->Sweep());
         page->Destroy();
     }
 }
 
-TEST(CustomAllocTest, MediumPageSweepSingleMarked) {
-    MediumPage* page = MediumPage::Create(MIN_BLOCK_SIZE);
+TEST(CustomAllocTest, NextFitPageSweepSingleMarked) {
+    NextFitPage* page = NextFitPage::Create(MIN_BLOCK_SIZE);
     mark(alloc(page, MIN_BLOCK_SIZE));
     EXPECT_TRUE(page->Sweep());
     page->Destroy();
 }
 
-TEST(CustomAllocTest, MediumPageSweepSingleReuse) {
+TEST(CustomAllocTest, NextFitPageSweepSingleReuse) {
     for (uint32_t seed = 0xC0FFEE0; seed <= 0xC0FFEEF; ++seed) {
         std::minstd_rand r(seed);
-        MediumPage* page = MediumPage::Create(MIN_BLOCK_SIZE);
+        NextFitPage* page = NextFitPage::Create(MIN_BLOCK_SIZE);
         int count1 = 0;
         while (alloc(page, MIN_BLOCK_SIZE + r() % 100)) ++count1;
         EXPECT_FALSE(page->Sweep());
@@ -88,10 +88,10 @@ TEST(CustomAllocTest, MediumPageSweepSingleReuse) {
     }
 }
 
-TEST(CustomAllocTest, MediumPageSweepReuse) {
+TEST(CustomAllocTest, NextFitPageSweepReuse) {
     for (uint32_t seed = 0xC0FFEE0; seed <= 0xC0FFEEF; ++seed) {
         std::minstd_rand r(seed);
-        MediumPage* page = MediumPage::Create(MIN_BLOCK_SIZE);
+        NextFitPage* page = NextFitPage::Create(MIN_BLOCK_SIZE);
         int unmarked = 0;
         while (true) {
             uint8_t* ptr = alloc(page, MIN_BLOCK_SIZE);
@@ -110,11 +110,11 @@ TEST(CustomAllocTest, MediumPageSweepReuse) {
     }
 }
 
-TEST(CustomAllocTest, MediumPageSweepCoallesce) {
-    MediumPage* page = MediumPage::Create(MIN_BLOCK_SIZE);
-    EXPECT_TRUE(alloc(page, (MEDIUM_PAGE_CELL_COUNT-1) / 2 - 1));
+TEST(CustomAllocTest, NextFitPageSweepCoallesce) {
+    NextFitPage* page = NextFitPage::Create(MIN_BLOCK_SIZE);
+    EXPECT_TRUE(alloc(page, (NEXT_FIT_PAGE_CELL_COUNT-1) / 2 - 1));
     EXPECT_FALSE(page->Sweep());
-    EXPECT_TRUE(alloc(page, (MEDIUM_PAGE_CELL_COUNT-1) - 1));
+    EXPECT_TRUE(alloc(page, (NEXT_FIT_PAGE_CELL_COUNT-1) - 1));
     page->Destroy();
 }
 
diff --git a/kotlin-native/runtime/src/custom_alloc/cpp/SingleObjectPage.cpp b/kotlin-native/runtime/src/custom_alloc/cpp/SingleObjectPage.cpp
new file mode 100644
index 00000000000..896c6922243
--- /dev/null
+++ b/kotlin-native/runtime/src/custom_alloc/cpp/SingleObjectPage.cpp
@@ -0,0 +1,47 @@
+/*
+ * Copyright 2022 JetBrains s.r.o. Use of this source code is governed by the Apache 2.0 license
+ * that can be found in the LICENSE file.
+ */
+
+#include "SingleObjectPage.hpp"
+
+#include <atomic>
+#include <cstdint>
+
+#include "CustomLogging.hpp"
+#include "CustomAllocConstants.hpp"
+#include "GCApi.hpp"
+
+namespace kotlin::alloc {
+
+SingleObjectPage* SingleObjectPage::Create(uint64_t cellCount) noexcept {
+    CustomAllocInfo("SingleObjectPage::Create(%" PRIu64 ")", cellCount);
+    RuntimeAssert(cellCount > NEXT_FIT_PAGE_MAX_BLOCK_SIZE, "blockSize too small for SingleObjectPage");
+    uint64_t size = sizeof(SingleObjectPage) + cellCount * sizeof(uint64_t);
+    return new (SafeAlloc(size)) SingleObjectPage();
+}
+
+void SingleObjectPage::Destroy() noexcept {
+    std_support::free(this);
+}
+
+uint8_t* SingleObjectPage::Data() noexcept {
+    return data_;
+}
+
+uint8_t* SingleObjectPage::TryAllocate() noexcept {
+    if (isAllocated_) return nullptr;
+    isAllocated_ = true;
+    return Data();
+}
+
+bool SingleObjectPage::Sweep() noexcept {
+    CustomAllocDebug("SingleObjectPage@%p::Sweep()", this);
+    if (!TryResetMark(Data())) {
+        isAllocated_ = false;
+        return false;
+    }
+    return true;
+}
+
+} // namespace kotlin::alloc
diff --git a/kotlin-native/runtime/src/custom_alloc/cpp/LargePage.hpp b/kotlin-native/runtime/src/custom_alloc/cpp/SingleObjectPage.hpp
similarity index 65%
rename from kotlin-native/runtime/src/custom_alloc/cpp/LargePage.hpp
rename to kotlin-native/runtime/src/custom_alloc/cpp/SingleObjectPage.hpp
index aad7992efb6..c42500bf233 100644
--- a/kotlin-native/runtime/src/custom_alloc/cpp/LargePage.hpp
+++ b/kotlin-native/runtime/src/custom_alloc/cpp/SingleObjectPage.hpp
@@ -3,20 +3,19 @@
  * that can be found in the LICENSE file.
  */
 
-#ifndef CUSTOM_ALLOC_CPP_LARGEPAGE_HPP_
-#define CUSTOM_ALLOC_CPP_LARGEPAGE_HPP_
+#ifndef CUSTOM_ALLOC_CPP_SINGLEOBJECTPAGE_HPP_
+#define CUSTOM_ALLOC_CPP_SINGLEOBJECTPAGE_HPP_
 
 #include <atomic>
 #include <cstdint>
 
 #include "AtomicStack.hpp"
-#include "MediumPage.hpp"
 
 namespace kotlin::alloc {
 
-class alignas(8) LargePage {
+class alignas(8) SingleObjectPage {
 public:
-    static LargePage* Create(uint64_t cellCount) noexcept;
+    static SingleObjectPage* Create(uint64_t cellCount) noexcept;
 
     void Destroy() noexcept;
 
@@ -27,8 +26,8 @@ public:
     bool Sweep() noexcept;
 
 private:
-    friend class AtomicStack<LargePage>;
-    LargePage* next_;
+    friend class AtomicStack<SingleObjectPage>;
+    SingleObjectPage* next_;
     bool isAllocated_ = false;
     struct alignas(8) {
         uint8_t data_[];
diff --git a/kotlin-native/runtime/src/custom_alloc/cpp/LargePageTest.cpp b/kotlin-native/runtime/src/custom_alloc/cpp/SingleObjectPageTest.cpp
similarity index 64%
rename from kotlin-native/runtime/src/custom_alloc/cpp/LargePageTest.cpp
rename to kotlin-native/runtime/src/custom_alloc/cpp/SingleObjectPageTest.cpp
index acde849d9ae..fb6f3764d93 100644
--- a/kotlin-native/runtime/src/custom_alloc/cpp/LargePageTest.cpp
+++ b/kotlin-native/runtime/src/custom_alloc/cpp/SingleObjectPageTest.cpp
@@ -8,38 +8,38 @@
 
 #include "CustomAllocConstants.hpp"
 #include "gtest/gtest.h"
-#include "LargePage.hpp"
+#include "SingleObjectPage.hpp"
 #include "TypeInfo.h"
 
 namespace {
 
-using LargePage = typename kotlin::alloc::LargePage;
+using SingleObjectPage = typename kotlin::alloc::SingleObjectPage;
 
 TypeInfo fakeType = {.flags_ = 0}; // a type without a finalizer
 
-#define MIN_BLOCK_SIZE MEDIUM_PAGE_CELL_COUNT
+#define MIN_BLOCK_SIZE NEXT_FIT_PAGE_CELL_COUNT
 
 void mark(void* obj) {
     reinterpret_cast<uint64_t*>(obj)[0] = 1;
 }
 
-LargePage* alloc(uint64_t blockSize) {
-    LargePage* page = LargePage::Create(blockSize);
+SingleObjectPage* alloc(uint64_t blockSize) {
+    SingleObjectPage* page = SingleObjectPage::Create(blockSize);
     uint64_t* ptr = reinterpret_cast<uint64_t*>(page->TryAllocate());
     memset(ptr, 0, 8 * blockSize);
     ptr[1] = reinterpret_cast<uint64_t>(&fakeType);
     return page;
 }
 
-TEST(CustomAllocTest, LargePageSweepEmptyPage) {
-    LargePage* page = alloc(MIN_BLOCK_SIZE);
+TEST(CustomAllocTest, SingleObjectPageSweepEmptyPage) {
+    SingleObjectPage* page = alloc(MIN_BLOCK_SIZE);
     EXPECT_TRUE(page);
     EXPECT_FALSE(page->Sweep());
     page->Destroy();
 }
 
-TEST(CustomAllocTest, LargePageSweepFullPage) {
-    LargePage* page = alloc(MIN_BLOCK_SIZE);
+TEST(CustomAllocTest, SingleObjectPageSweepFullPage) {
+    SingleObjectPage* page = alloc(MIN_BLOCK_SIZE);
     EXPECT_TRUE(page);
     EXPECT_TRUE(page->Data());
     mark(page->Data());
diff --git a/kotlin-native/runtime/src/custom_alloc/cpp/SmallPage.cpp b/kotlin-native/runtime/src/custom_alloc/cpp/SmallPage.cpp
deleted file mode 100644
index f35e01c56e7..00000000000
--- a/kotlin-native/runtime/src/custom_alloc/cpp/SmallPage.cpp
+++ /dev/null
@@ -1,76 +0,0 @@
-/*
- * Copyright 2022 JetBrains s.r.o. Use of this source code is governed by the Apache 2.0 license
- * that can be found in the LICENSE file.
- */
-
-#include "SmallPage.hpp"
-
-#include <atomic>
-#include <cstdint>
-#include <cstring>
-#include <random>
-
-#include "CustomLogging.hpp"
-#include "CustomAllocConstants.hpp"
-#include "GCApi.hpp"
-
-namespace kotlin::alloc {
-
-SmallPage* SmallPage::Create(uint32_t blockSize) noexcept {
-    CustomAllocInfo("SmallPage::Create(%u)", blockSize);
-    RuntimeAssert(blockSize <= SMALL_PAGE_MAX_BLOCK_SIZE, "blockSize too large for small page");
-    return new (SafeAlloc(SMALL_PAGE_SIZE)) SmallPage(blockSize);
-}
-
-void SmallPage::Destroy() noexcept {
-    std_support::free(this);
-}
-
-SmallPage::SmallPage(uint32_t blockSize) noexcept : blockSize_(blockSize) {
-    CustomAllocInfo("SmallPage(%p)::SmallPage(%u)", this, blockSize);
-    nextFree_ = cells_;
-    SmallCell* end = cells_ + (SMALL_PAGE_CELL_COUNT + 1 - blockSize_);
-    for (SmallCell* cell = cells_; cell < end; cell = cell->nextFree) {
-        cell->nextFree = cell + blockSize;
-    }
-}
-
-uint8_t* SmallPage::TryAllocate() noexcept {
-    SmallCell* end = cells_ + (SMALL_PAGE_CELL_COUNT + 1 - blockSize_);
-    SmallCell* freeBlock = nextFree_;
-    if (freeBlock >= end) {
-        return nullptr;
-    }
-    nextFree_ = freeBlock->nextFree;
-    CustomAllocDebug("SmallPage(%p){%u}::TryAllocate() = %p", this, blockSize_, freeBlock);
-    return freeBlock->data;
-}
-
-bool SmallPage::Sweep() noexcept {
-    CustomAllocInfo("SmallPage(%p)::Sweep()", this);
-    // `end` is after the last legal allocation of a block, but does not
-    // necessarily match an actual block starting point.
-    SmallCell* end = cells_ + (SMALL_PAGE_CELL_COUNT + 1 - blockSize_);
-    bool alive = false;
-    SmallCell** nextFree = &nextFree_;
-    for (SmallCell* cell = cells_; cell < end; cell += blockSize_) {
-        // If the current cell is free, move on.
-        if (cell == *nextFree) {
-            nextFree = &cell->nextFree;
-            continue;
-        }
-        // If the current cell was marked, it's alive, and the whole page is alive.
-        if (TryResetMark(cell)) {
-            alive = true;
-            continue;
-        }
-        CustomAllocInfo("SmallPage(%p)::Sweep: reclaim %p", this, cell);
-        // Free the current block and insert it into the free list.
-        cell->nextFree = *nextFree;
-        *nextFree = cell;
-        nextFree = &cell->nextFree;
-    }
-    return alive;
-}
-
-} // namespace kotlin::alloc