diff --git a/compiler/backend/src/org/jetbrains/kotlin/codegen/state/KotlinTypeMapper.java b/compiler/backend/src/org/jetbrains/kotlin/codegen/state/KotlinTypeMapper.java
index 28fa6166b49..9ba6a9ccaca 100644
--- a/compiler/backend/src/org/jetbrains/kotlin/codegen/state/KotlinTypeMapper.java
+++ b/compiler/backend/src/org/jetbrains/kotlin/codegen/state/KotlinTypeMapper.java
@@ -969,8 +969,12 @@ public class KotlinTypeMapper {
             }
 
             for (ValueParameterDescriptor parameter : valueParameters) {
-                if (writeCustomParameter(f, parameter, sw)) continue;
-                writeParameter(sw, parameter.getType(), f);
+                boolean forceBoxing = MethodSignatureMappingKt.forceSingleValueParameterBoxing(f);
+                writeParameter(
+                        sw,
+                        forceBoxing ? TypeUtils.makeNullable(parameter.getType()) : parameter.getType(),
+                        f
+                );
             }
 
             sw.writeReturnType();
@@ -1020,24 +1024,6 @@ public class KotlinTypeMapper {
         }
     }
 
-    private boolean writeCustomParameter(
-            @NotNull FunctionDescriptor f,
-            @NotNull ValueParameterDescriptor parameter,
-            @NotNull JvmSignatureWriter sw
-    ) {
-        FunctionDescriptor overridden =
-                BuiltinMethodsWithSpecialGenericSignature.getOverriddenBuiltinFunctionWithErasedValueParametersInJava(f);
-        if (overridden == null) return false;
-        if (SpecialBuiltinMembers.isFromJavaOrBuiltins(f)) return false;
-
-        if (overridden.getName().asString().equals("remove") && mapType(parameter.getType()).getSort() == Type.INT) {
-            writeParameter(sw, TypeUtils.makeNullable(parameter.getType()), f);
-            return true;
-        }
-
-        return false;
-    }
-
     @NotNull
     private static String getDefaultDescriptor(@NotNull Method method, @Nullable String dispatchReceiverDescriptor, boolean isExtension) {
         String descriptor = method.getDescriptor();
diff --git a/compiler/testData/codegen/boxAgainstJava/platformTypes/specializedMapFull.kt b/compiler/testData/codegen/boxAgainstJava/platformTypes/specializedMapFull.kt
new file mode 100644
index 00000000000..6829b8262f8
--- /dev/null
+++ b/compiler/testData/codegen/boxAgainstJava/platformTypes/specializedMapFull.kt
@@ -0,0 +1,119 @@
+// FILE: AbstractSpecializedMap.java
+public abstract class AbstractSpecializedMap implements java.util.Map<Integer, Double> {
+    public abstract double put(int x, double y);
+    public abstract double remove(int k);
+    public abstract double get(int k);
+
+    public abstract boolean containsKey(int k);
+    public boolean containsKey(Object x) {
+        return false;
+    }
+
+    public abstract boolean containsValue(double v);
+    public boolean containsValue(Object x) {
+        return false;
+    }
+}
+
+// FILE: SpecializedMap.java
+import org.jetbrains.annotations.NotNull;
+
+import java.util.Collection;
+import java.util.Map;
+import java.util.Set;
+
+public class SpecializedMap extends AbstractSpecializedMap {
+    public double put(int x, double y) {
+        return 123.0;
+    }
+
+    @Override
+    public Double get(Object key) {
+        return null;
+    }
+
+    @Override
+    public Double put(Integer key, Double value) {
+        return null;
+    }
+
+    public double remove(int k) {
+        return 456.0;
+    }
+
+
+    public Double remove(Object ok) {
+        return null;
+    }
+
+
+    public double get(int k) {
+        return 789.0;
+    }
+
+    public boolean containsKey(int k) {
+        return true;
+    }
+
+    public boolean containsValue(double v) {
+        return true;
+    }
+
+    @Override
+    public void putAll(Map<? extends Integer, ? extends Double> m) {
+    }
+
+    @Override
+    public void clear() {
+
+    }
+
+    @NotNull
+    @Override
+    public Set<Integer> keySet() {
+        return null;
+    }
+
+    @NotNull
+    @Override
+    public Collection<Double> values() {
+        return null;
+    }
+
+    @NotNull
+    @Override
+    public Set<Entry<Integer, Double>> entrySet() {
+        return null;
+    }
+
+    @Override
+    public int size() {
+        return 0;
+    }
+
+    @Override
+    public boolean isEmpty() {
+        return false;
+    }
+}
+
+// FILE: main.kt
+fun box(): String {
+    val x = SpecializedMap()
+    if (!x.containsKey(1)) return "fail 1"
+    if (x.containsKey(null)) return "fail 2"
+
+    if (!x.containsValue(2.0)) return "fail 3"
+    if (x.containsValue(null)) return "fail 4"
+
+    if (x.put(1, 5.0) != 123.0) return "fail 5"
+    if (x.put(1, null) != null) return "fail 6"
+
+    if (x.remove(1) != 456.0) return "fail 7"
+    if (x.remove(null) != null) return "fail 8"
+
+    if (x.get(1) != 789.0) return "fail 9"
+    if (x.get(null) != null) return "fail 10"
+
+    return "OK"
+}
diff --git a/compiler/testData/codegen/boxAgainstJava/platformTypes/specializedMapPut.kt b/compiler/testData/codegen/boxAgainstJava/platformTypes/specializedMapPut.kt
new file mode 100644
index 00000000000..abeca9a65b3
--- /dev/null
+++ b/compiler/testData/codegen/boxAgainstJava/platformTypes/specializedMapPut.kt
@@ -0,0 +1,21 @@
+// FILE: A.java
+import java.util.HashMap;
+
+public class A extends HashMap<Integer, Double> {
+    public double put(int x, double y) {
+        return 1.0;
+    }
+
+    @Override
+    public Double put(Integer key, Double value) {
+        return super.put(key, value);
+    }
+}
+
+// FILE: main.kt
+fun box(): String {
+    val o = A()
+    o.put(1, 2.0)
+
+    return "OK"
+}
diff --git a/compiler/testData/diagnostics/tests/j+k/primitiveOverrides/kt11140.kt b/compiler/testData/diagnostics/tests/j+k/primitiveOverrides/kt11140.kt
new file mode 100644
index 00000000000..9fc2f5446c7
--- /dev/null
+++ b/compiler/testData/diagnostics/tests/j+k/primitiveOverrides/kt11140.kt
@@ -0,0 +1,23 @@
+// FILE: B.java
+public interface B<T1, T2> {
+    double put(int x, double y);
+    T2 put(T1 x, T2 y);
+}
+// FILE: A.java
+import java.util.HashMap;
+
+public class A extends HashMap<Integer, Double> implements B<Integer, Double> {
+    public double put(int x, double y) {
+        return 1.0;
+    }
+
+    @Override
+    public Double put(Integer key, Double value) {
+        return super.put(key, value);
+    }
+}
+// FILE: main.kt
+fun test(){
+    val o = A()
+    o.put(1, 2.0)
+}
diff --git a/compiler/testData/diagnostics/tests/j+k/primitiveOverrides/kt11140.txt b/compiler/testData/diagnostics/tests/j+k/primitiveOverrides/kt11140.txt
new file mode 100644
index 00000000000..300490dcd06
--- /dev/null
+++ b/compiler/testData/diagnostics/tests/j+k/primitiveOverrides/kt11140.txt
@@ -0,0 +1,73 @@
+package
+
+public fun test(): kotlin.Unit
+
+public open class A : java.util.HashMap<kotlin.Int!, kotlin.Double!>, B<kotlin.Int!, kotlin.Double!> {
+    public constructor A()
+    public open override /*1*/ /*fake_override*/ val entries: kotlin.collections.MutableSet<kotlin.collections.MutableMap.MutableEntry<kotlin.Int!, kotlin.Double!>>
+    invisible_fake final override /*1*/ /*fake_override*/ var entrySet: kotlin.collections.(Mutable)Set<kotlin.collections.(Mutable)Map.(Mutable)Entry<kotlin.Int!, kotlin.Double!>!>!
+    invisible_fake final override /*1*/ /*fake_override*/ val hashSeed: kotlin.Int
+    invisible_fake final override /*1*/ /*fake_override*/ var keySet: kotlin.collections.(Mutable)Set<kotlin.Int!>!
+    public open override /*1*/ /*fake_override*/ val keys: kotlin.collections.MutableSet<kotlin.Int!>
+    invisible_fake final override /*1*/ /*fake_override*/ val loadFactor: kotlin.Float
+    invisible_fake final override /*1*/ /*fake_override*/ var modCount: kotlin.Int
+    invisible_fake final override /*1*/ /*fake_override*/ var size: kotlin.Int
+    public open override /*1*/ /*fake_override*/ val size: kotlin.Int
+    invisible_fake final override /*1*/ /*fake_override*/ var table: kotlin.Array<(out) java.util.HashMap.Entry<kotlin.Int!, kotlin.Double!>!>!
+    invisible_fake final override /*1*/ /*fake_override*/ var threshold: kotlin.Int
+    invisible_fake final override /*1*/ /*fake_override*/ var useAltHashing: kotlin.Boolean
+    invisible_fake final override /*1*/ /*fake_override*/ var values: kotlin.collections.(Mutable)Collection<kotlin.Double!>!
+    public open override /*1*/ /*fake_override*/ val values: kotlin.collections.MutableCollection<kotlin.Double!>
+    invisible_fake open override /*1*/ /*fake_override*/ fun addEntry(/*0*/ p0: kotlin.Int, /*1*/ p1: kotlin.Int!, /*2*/ p2: kotlin.Double!, /*3*/ p3: kotlin.Int): kotlin.Unit
+    invisible_fake open override /*1*/ /*fake_override*/ fun capacity(): kotlin.Int
+    public open override /*1*/ /*fake_override*/ fun clear(): kotlin.Unit
+    public open override /*1*/ /*fake_override*/ fun clone(): kotlin.Any
+    public open override /*1*/ /*fake_override*/ fun containsKey(/*0*/ key: kotlin.Int!): kotlin.Boolean
+    invisible_fake open override /*1*/ /*fake_override*/ fun containsNullValue(): kotlin.Boolean
+    public open override /*1*/ /*fake_override*/ fun containsValue(/*0*/ value: kotlin.Double!): kotlin.Boolean
+    invisible_fake open override /*1*/ /*fake_override*/ fun createEntry(/*0*/ p0: kotlin.Int, /*1*/ p1: kotlin.Int!, /*2*/ p2: kotlin.Double!, /*3*/ p3: kotlin.Int): kotlin.Unit
+    invisible_fake open override /*1*/ /*fake_override*/ fun entrySet0(): kotlin.collections.(Mutable)Set<kotlin.collections.(Mutable)Map.(Mutable)Entry<kotlin.Int!, kotlin.Double!>!>!
+    public open override /*2*/ /*fake_override*/ fun equals(/*0*/ other: kotlin.Any?): kotlin.Boolean
+    public open override /*1*/ /*fake_override*/ fun get(/*0*/ key: kotlin.Int!): kotlin.Double?
+    invisible_fake final override /*1*/ /*fake_override*/ fun getEntry(/*0*/ p0: kotlin.Any!): java.util.HashMap.Entry<kotlin.Int!, kotlin.Double!>!
+    invisible_fake open override /*1*/ /*fake_override*/ fun getForNullKey(): kotlin.Double!
+    invisible_fake final override /*1*/ /*fake_override*/ fun hash(/*0*/ p0: kotlin.Any!): kotlin.Int
+    public open override /*2*/ /*fake_override*/ fun hashCode(): kotlin.Int
+    invisible_fake open override /*1*/ /*fake_override*/ fun init(): kotlin.Unit
+    public open override /*1*/ /*fake_override*/ fun isEmpty(): kotlin.Boolean
+    invisible_fake open override /*1*/ /*fake_override*/ fun loadFactor(): kotlin.Float
+    invisible_fake open override /*1*/ /*fake_override*/ fun newEntryIterator(): kotlin.collections.(Mutable)Iterator<kotlin.collections.(Mutable)Map.(Mutable)Entry<kotlin.Int!, kotlin.Double!>!>!
+    invisible_fake open override /*1*/ /*fake_override*/ fun newKeyIterator(): kotlin.collections.(Mutable)Iterator<kotlin.Int!>!
+    invisible_fake open override /*1*/ /*fake_override*/ fun newValueIterator(): kotlin.collections.(Mutable)Iterator<kotlin.Double!>!
+    public open override /*1*/ fun put(/*0*/ x: kotlin.Int, /*1*/ y: kotlin.Double): kotlin.Double
+    @java.lang.Override() public open override /*2*/ fun put(/*0*/ key: kotlin.Int!, /*1*/ value: kotlin.Double!): kotlin.Double?
+    public open override /*1*/ /*fake_override*/ fun putAll(/*0*/ from: kotlin.collections.Map<out kotlin.Int!, kotlin.Double!>): kotlin.Unit
+    invisible_fake open override /*1*/ /*fake_override*/ fun putAllForCreate(/*0*/ p0: (kotlin.collections.MutableMap<out kotlin.Int!, out kotlin.Double!>..kotlin.collections.Map<out kotlin.Int!, kotlin.Double!>?)): kotlin.Unit
+    invisible_fake open override /*1*/ /*fake_override*/ fun putForCreate(/*0*/ p0: kotlin.Int!, /*1*/ p1: kotlin.Double!): kotlin.Unit
+    invisible_fake open override /*1*/ /*fake_override*/ fun putForNullKey(/*0*/ p0: kotlin.Double!): kotlin.Double!
+    invisible_fake open override /*1*/ /*fake_override*/ fun readObject(/*0*/ p0: java.io.ObjectInputStream!): kotlin.Unit
+    public open override /*1*/ /*fake_override*/ fun remove(/*0*/ key: kotlin.Int!): kotlin.Double?
+    invisible_fake final override /*1*/ /*fake_override*/ fun removeEntryForKey(/*0*/ p0: kotlin.Any!): java.util.HashMap.Entry<kotlin.Int!, kotlin.Double!>!
+    invisible_fake final override /*1*/ /*fake_override*/ fun removeMapping(/*0*/ p0: kotlin.Any!): java.util.HashMap.Entry<kotlin.Int!, kotlin.Double!>!
+    invisible_fake open override /*1*/ /*fake_override*/ fun resize(/*0*/ p0: kotlin.Int): kotlin.Unit
+    public open override /*2*/ /*fake_override*/ fun toString(): kotlin.String
+    invisible_fake open override /*1*/ /*fake_override*/ fun transfer(/*0*/ p0: kotlin.Array<(out) java.util.HashMap.Entry<(raw) kotlin.Any!, (raw) kotlin.Any!>!>!, /*1*/ p1: kotlin.Boolean): kotlin.Unit
+    invisible_fake open override /*1*/ /*fake_override*/ fun writeObject(/*0*/ p0: java.io.ObjectOutputStream!): kotlin.Unit
+
+    // Static members
+    invisible_fake const final override /*1*/ /*fake_override*/ val ALTERNATIVE_HASHING_THRESHOLD_DEFAULT: kotlin.Int
+    invisible_fake const final override /*1*/ /*fake_override*/ val DEFAULT_INITIAL_CAPACITY: kotlin.Int
+    invisible_fake const final override /*1*/ /*fake_override*/ val DEFAULT_LOAD_FACTOR: kotlin.Float
+    invisible_fake const final override /*1*/ /*fake_override*/ val MAXIMUM_CAPACITY: kotlin.Int
+    invisible_fake const final override /*1*/ /*fake_override*/ val serialVersionUID: kotlin.Long
+    invisible_fake open override /*1*/ /*fake_override*/ fun eq(/*0*/ p0: kotlin.Any!, /*1*/ p1: kotlin.Any!): kotlin.Boolean
+    invisible_fake open override /*1*/ /*fake_override*/ fun indexFor(/*0*/ p0: kotlin.Int, /*1*/ p1: kotlin.Int): kotlin.Int
+}
+
+public interface B</*0*/ T1 : kotlin.Any!, /*1*/ T2 : kotlin.Any!> {
+    public open override /*1*/ /*fake_override*/ fun equals(/*0*/ other: kotlin.Any?): kotlin.Boolean
+    public open override /*1*/ /*fake_override*/ fun hashCode(): kotlin.Int
+    public abstract fun put(/*0*/ x: T1!, /*1*/ y: T2!): T2!
+    public abstract fun put(/*0*/ x: kotlin.Int, /*1*/ y: kotlin.Double): kotlin.Double
+    public open override /*1*/ /*fake_override*/ fun toString(): kotlin.String
+}
diff --git a/compiler/testData/diagnostics/tests/j+k/primitiveOverrides/notNullAnnotated.kt b/compiler/testData/diagnostics/tests/j+k/primitiveOverrides/notNullAnnotated.kt
new file mode 100644
index 00000000000..36ce0a1aa39
--- /dev/null
+++ b/compiler/testData/diagnostics/tests/j+k/primitiveOverrides/notNullAnnotated.kt
@@ -0,0 +1,22 @@
+// FILE: A.java
+import org.jetbrains.annotations.*;
+
+public class A {
+    public void foo(int x) {}
+    public void bar(@NotNull Double x) {}
+}
+
+// FILE: B.java
+import org.jetbrains.annotations.*;
+public class B extends A {
+    public void foo(@NotNull Integer x) {}
+    public void bar(double x) {}
+}
+
+// FILE: main.kt
+
+fun foo(b: B) {
+    // See KT-9182
+    b.<!OVERLOAD_RESOLUTION_AMBIGUITY!>foo<!>(1)
+    b.<!OVERLOAD_RESOLUTION_AMBIGUITY!>bar<!>(2.0)
+}
diff --git a/compiler/testData/diagnostics/tests/j+k/primitiveOverrides/notNullAnnotated.txt b/compiler/testData/diagnostics/tests/j+k/primitiveOverrides/notNullAnnotated.txt
new file mode 100644
index 00000000000..cc1dbdf050b
--- /dev/null
+++ b/compiler/testData/diagnostics/tests/j+k/primitiveOverrides/notNullAnnotated.txt
@@ -0,0 +1,23 @@
+package
+
+public fun foo(/*0*/ b: B): kotlin.Unit
+
+public open class A {
+    public constructor A()
+    public open fun bar(/*0*/ @org.jetbrains.annotations.NotNull() x: kotlin.Double): kotlin.Unit
+    public open override /*1*/ /*fake_override*/ fun equals(/*0*/ other: kotlin.Any?): kotlin.Boolean
+    public open fun foo(/*0*/ x: kotlin.Int): kotlin.Unit
+    public open override /*1*/ /*fake_override*/ fun hashCode(): kotlin.Int
+    public open override /*1*/ /*fake_override*/ fun toString(): kotlin.String
+}
+
+public open class B : A {
+    public constructor B()
+    public open fun bar(/*0*/ x: kotlin.Double): kotlin.Unit
+    public open override /*1*/ /*fake_override*/ fun bar(/*0*/ @org.jetbrains.annotations.NotNull() x: kotlin.Double): kotlin.Unit
+    public open override /*1*/ /*fake_override*/ fun equals(/*0*/ other: kotlin.Any?): kotlin.Boolean
+    public open fun foo(/*0*/ @org.jetbrains.annotations.NotNull() x: kotlin.Int): kotlin.Unit
+    public open override /*1*/ /*fake_override*/ fun foo(/*0*/ x: kotlin.Int): kotlin.Unit
+    public open override /*1*/ /*fake_override*/ fun hashCode(): kotlin.Int
+    public open override /*1*/ /*fake_override*/ fun toString(): kotlin.String
+}
diff --git a/compiler/testData/diagnostics/tests/j+k/primitiveOverrides/specializedMap.kt b/compiler/testData/diagnostics/tests/j+k/primitiveOverrides/specializedMap.kt
new file mode 100644
index 00000000000..1aaaa82660d
--- /dev/null
+++ b/compiler/testData/diagnostics/tests/j+k/primitiveOverrides/specializedMap.kt
@@ -0,0 +1,113 @@
+// FILE: AbstractSpecializedMap.java
+public abstract class AbstractSpecializedMap implements java.util.Map<Integer, Double> {
+    public abstract double put(int x, double y);
+    public abstract double remove(int k);
+    public abstract double get(int k);
+
+    public abstract boolean containsKey(int k);
+    public boolean containsKey(Object x) {
+        return false;
+    }
+
+    public abstract boolean containsValue(double v);
+    public boolean containsValue(Object x) {
+        return false;
+    }
+}
+
+// FILE: SpecializedMap.java
+import org.jetbrains.annotations.NotNull;
+
+import java.util.Collection;
+import java.util.Map;
+import java.util.Set;
+
+public class SpecializedMap extends AbstractSpecializedMap {
+    public double put(int x, double y) {
+        return 123.0;
+    }
+
+    @Override
+    public Double get(Object key) {
+        return null;
+    }
+
+    @Override
+    public Double put(Integer key, Double value) {
+        return null;
+    }
+
+    public double remove(int k) {
+        return 456.0;
+    }
+
+
+    public Double remove(Object ok) {
+        return null;
+    }
+
+
+    public double get(int k) {
+        return 789.0;
+    }
+
+    public boolean containsKey(int k) {
+        return true;
+    }
+
+    public boolean containsValue(double v) {
+        return true;
+    }
+
+    @Override
+    public void putAll(Map<? extends Integer, ? extends Double> m) {
+    }
+
+    @Override
+    public void clear() {
+
+    }
+
+    @NotNull
+    @Override
+    public Set<Integer> keySet() {
+        return null;
+    }
+
+    @NotNull
+    @Override
+    public Collection<Double> values() {
+        return null;
+    }
+
+    @NotNull
+    @Override
+    public Set<Entry<Integer, Double>> entrySet() {
+        return null;
+    }
+
+    @Override
+    public int size() {
+        return 0;
+    }
+
+    @Override
+    public boolean isEmpty() {
+        return false;
+    }
+}
+
+// FILE: main.kt
+fun foo(x: SpecializedMap) {
+    x.containsKey(1)
+    x.containsKey(null)
+
+    x.get(2)
+    x.get(null)
+
+    x.remove(3)
+    x.remove(null)
+
+    x.put(4, 5.0)
+    x.put(4, null)
+}
diff --git a/compiler/testData/diagnostics/tests/j+k/primitiveOverrides/specializedMap.txt b/compiler/testData/diagnostics/tests/j+k/primitiveOverrides/specializedMap.txt
new file mode 100644
index 00000000000..2dd6f367098
--- /dev/null
+++ b/compiler/testData/diagnostics/tests/j+k/primitiveOverrides/specializedMap.txt
@@ -0,0 +1,51 @@
+package
+
+public fun foo(/*0*/ x: SpecializedMap): kotlin.Unit
+
+public abstract class AbstractSpecializedMap : kotlin.collections.MutableMap<kotlin.Int!, kotlin.Double!> {
+    public constructor AbstractSpecializedMap()
+    public abstract override /*1*/ /*fake_override*/ val entries: kotlin.collections.MutableSet<kotlin.collections.MutableMap.MutableEntry<kotlin.Int!, kotlin.Double!>>
+    public abstract override /*1*/ /*fake_override*/ val keys: kotlin.collections.MutableSet<kotlin.Int!>
+    public abstract override /*1*/ /*fake_override*/ val size: kotlin.Int
+    public abstract override /*1*/ /*fake_override*/ val values: kotlin.collections.MutableCollection<kotlin.Double!>
+    public abstract override /*1*/ /*fake_override*/ fun clear(): kotlin.Unit
+    public abstract fun containsKey(/*0*/ k: kotlin.Int): kotlin.Boolean
+    public open override /*1*/ fun containsKey(/*0*/ x: kotlin.Int!): kotlin.Boolean
+    public abstract fun containsValue(/*0*/ v: kotlin.Double): kotlin.Boolean
+    public open override /*1*/ fun containsValue(/*0*/ x: kotlin.Double!): kotlin.Boolean
+    public open override /*1*/ /*fake_override*/ fun equals(/*0*/ other: kotlin.Any?): kotlin.Boolean
+    public abstract operator fun get(/*0*/ k: kotlin.Int): kotlin.Double
+    public abstract override /*1*/ /*fake_override*/ fun get(/*0*/ key: kotlin.Int!): kotlin.Double?
+    public open override /*1*/ /*fake_override*/ fun hashCode(): kotlin.Int
+    public abstract override /*1*/ /*fake_override*/ fun isEmpty(): kotlin.Boolean
+    public abstract fun put(/*0*/ x: kotlin.Int, /*1*/ y: kotlin.Double): kotlin.Double
+    public abstract override /*1*/ /*fake_override*/ fun put(/*0*/ key: kotlin.Int!, /*1*/ value: kotlin.Double!): kotlin.Double?
+    public abstract override /*1*/ /*fake_override*/ fun putAll(/*0*/ from: kotlin.collections.Map<out kotlin.Int!, kotlin.Double!>): kotlin.Unit
+    public abstract fun remove(/*0*/ k: kotlin.Int): kotlin.Double
+    public abstract override /*1*/ /*fake_override*/ fun remove(/*0*/ key: kotlin.Int!): kotlin.Double?
+    public open override /*1*/ /*fake_override*/ fun toString(): kotlin.String
+}
+
+public open class SpecializedMap : AbstractSpecializedMap {
+    public constructor SpecializedMap()
+    public open override /*1*/ val entries: kotlin.collections.MutableSet<kotlin.collections.MutableMap.MutableEntry<kotlin.Int!, kotlin.Double!>>
+    public open override /*1*/ val keys: kotlin.collections.MutableSet<kotlin.Int!>
+    public open override /*1*/ val size: kotlin.Int
+    public open override /*1*/ val values: kotlin.collections.MutableCollection<kotlin.Double!>
+    @java.lang.Override() public open override /*1*/ fun clear(): kotlin.Unit
+    public open override /*1*/ fun containsKey(/*0*/ k: kotlin.Int): kotlin.Boolean
+    public open override /*1*/ /*fake_override*/ fun containsKey(/*0*/ x: kotlin.Int!): kotlin.Boolean
+    public open override /*1*/ fun containsValue(/*0*/ v: kotlin.Double): kotlin.Boolean
+    public open override /*1*/ /*fake_override*/ fun containsValue(/*0*/ x: kotlin.Double!): kotlin.Boolean
+    public open override /*1*/ /*fake_override*/ fun equals(/*0*/ other: kotlin.Any?): kotlin.Boolean
+    public open override /*1*/ fun get(/*0*/ k: kotlin.Int): kotlin.Double
+    @java.lang.Override() public open override /*1*/ fun get(/*0*/ key: kotlin.Int!): kotlin.Double?
+    public open override /*1*/ /*fake_override*/ fun hashCode(): kotlin.Int
+    @java.lang.Override() public open override /*1*/ fun isEmpty(): kotlin.Boolean
+    public open override /*1*/ fun put(/*0*/ x: kotlin.Int, /*1*/ y: kotlin.Double): kotlin.Double
+    @java.lang.Override() public open override /*1*/ fun put(/*0*/ key: kotlin.Int!, /*1*/ value: kotlin.Double!): kotlin.Double?
+    @java.lang.Override() public open override /*1*/ fun putAll(/*0*/ from: kotlin.collections.Map<out kotlin.Int!, kotlin.Double!>): kotlin.Unit
+    public open override /*1*/ fun remove(/*0*/ k: kotlin.Int): kotlin.Double
+    public open override /*1*/ fun remove(/*0*/ ok: kotlin.Int!): kotlin.Double?
+    public open override /*1*/ /*fake_override*/ fun toString(): kotlin.String
+}
diff --git a/compiler/tests/org/jetbrains/kotlin/checkers/DiagnosticsTestGenerated.java b/compiler/tests/org/jetbrains/kotlin/checkers/DiagnosticsTestGenerated.java
index ccb8906f76d..939a2a32f42 100644
--- a/compiler/tests/org/jetbrains/kotlin/checkers/DiagnosticsTestGenerated.java
+++ b/compiler/tests/org/jetbrains/kotlin/checkers/DiagnosticsTestGenerated.java
@@ -11118,6 +11118,33 @@ public class DiagnosticsTestGenerated extends AbstractDiagnosticsTest {
                 }
             }
 
+            @TestMetadata("compiler/testData/diagnostics/tests/j+k/primitiveOverrides")
+            @TestDataPath("$PROJECT_ROOT")
+            @RunWith(JUnit3RunnerWithInners.class)
+            public static class PrimitiveOverrides extends AbstractDiagnosticsTest {
+                public void testAllFilesPresentInPrimitiveOverrides() throws Exception {
+                    KotlinTestUtils.assertAllTestsPresentByMetadata(this.getClass(), new File("compiler/testData/diagnostics/tests/j+k/primitiveOverrides"), Pattern.compile("^(.+)\\.kt$"), true);
+                }
+
+                @TestMetadata("kt11140.kt")
+                public void testKt11140() throws Exception {
+                    String fileName = KotlinTestUtils.navigationMetadata("compiler/testData/diagnostics/tests/j+k/primitiveOverrides/kt11140.kt");
+                    doTest(fileName);
+                }
+
+                @TestMetadata("notNullAnnotated.kt")
+                public void testNotNullAnnotated() throws Exception {
+                    String fileName = KotlinTestUtils.navigationMetadata("compiler/testData/diagnostics/tests/j+k/primitiveOverrides/notNullAnnotated.kt");
+                    doTest(fileName);
+                }
+
+                @TestMetadata("specializedMap.kt")
+                public void testSpecializedMap() throws Exception {
+                    String fileName = KotlinTestUtils.navigationMetadata("compiler/testData/diagnostics/tests/j+k/primitiveOverrides/specializedMap.kt");
+                    doTest(fileName);
+                }
+            }
+
             @TestMetadata("compiler/testData/diagnostics/tests/j+k/properties")
             @TestDataPath("$PROJECT_ROOT")
             @RunWith(JUnit3RunnerWithInners.class)
diff --git a/compiler/tests/org/jetbrains/kotlin/codegen/BlackBoxAgainstJavaCodegenTestGenerated.java b/compiler/tests/org/jetbrains/kotlin/codegen/BlackBoxAgainstJavaCodegenTestGenerated.java
index 99315396b8c..13b39e298e3 100644
--- a/compiler/tests/org/jetbrains/kotlin/codegen/BlackBoxAgainstJavaCodegenTestGenerated.java
+++ b/compiler/tests/org/jetbrains/kotlin/codegen/BlackBoxAgainstJavaCodegenTestGenerated.java
@@ -366,6 +366,18 @@ public class BlackBoxAgainstJavaCodegenTestGenerated extends AbstractBlackBoxAga
             String fileName = KotlinTestUtils.navigationMetadata("compiler/testData/codegen/boxAgainstJava/platformTypes/genericUnit.kt");
             doTest(fileName);
         }
+
+        @TestMetadata("specializedMapFull.kt")
+        public void testSpecializedMapFull() throws Exception {
+            String fileName = KotlinTestUtils.navigationMetadata("compiler/testData/codegen/boxAgainstJava/platformTypes/specializedMapFull.kt");
+            doTest(fileName);
+        }
+
+        @TestMetadata("specializedMapPut.kt")
+        public void testSpecializedMapPut() throws Exception {
+            String fileName = KotlinTestUtils.navigationMetadata("compiler/testData/codegen/boxAgainstJava/platformTypes/specializedMapPut.kt");
+            doTest(fileName);
+        }
     }
 
     @TestMetadata("compiler/testData/codegen/boxAgainstJava/property")
diff --git a/core/descriptor.loader.java/src/org/jetbrains/kotlin/load/java/JavaIncompatibilityRulesOverridabilityCondition.kt b/core/descriptor.loader.java/src/org/jetbrains/kotlin/load/java/JavaIncompatibilityRulesOverridabilityCondition.kt
index b1fe5c591f4..5cdab84e488 100644
--- a/core/descriptor.loader.java/src/org/jetbrains/kotlin/load/java/JavaIncompatibilityRulesOverridabilityCondition.kt
+++ b/core/descriptor.loader.java/src/org/jetbrains/kotlin/load/java/JavaIncompatibilityRulesOverridabilityCondition.kt
@@ -16,15 +16,19 @@
 
 package org.jetbrains.kotlin.load.java
 
+import org.jetbrains.kotlin.builtins.KotlinBuiltIns
 import org.jetbrains.kotlin.descriptors.*
 import org.jetbrains.kotlin.load.java.BuiltinMethodsWithDifferentJvmName.sameAsRenamedInJvmBuiltin
 import org.jetbrains.kotlin.load.java.BuiltinMethodsWithSpecialGenericSignature.sameAsBuiltinMethodWithErasedValueParameters
 import org.jetbrains.kotlin.load.java.descriptors.JavaClassDescriptor
 import org.jetbrains.kotlin.load.java.descriptors.JavaMethodDescriptor
+import org.jetbrains.kotlin.load.kotlin.JvmType
+import org.jetbrains.kotlin.load.kotlin.forceSingleValueParameterBoxing
+import org.jetbrains.kotlin.load.kotlin.mapToJvmType
 import org.jetbrains.kotlin.resolve.ExternalOverridabilityCondition
 import org.jetbrains.kotlin.resolve.ExternalOverridabilityCondition.Result
-import org.jetbrains.kotlin.resolve.OverridingUtil
-import org.jetbrains.kotlin.resolve.descriptorUtil.isDocumentedAnnotation
+import org.jetbrains.kotlin.resolve.descriptorUtil.fqNameSafe
+import org.jetbrains.kotlin.types.typeUtil.makeNullable
 
 /**
  * This class contains Java-related overridability conditions that may force incompatibility
@@ -39,6 +43,10 @@ class JavaIncompatibilityRulesOverridabilityCondition : ExternalOverridabilityCo
             return Result.INCOMPATIBLE
         }
 
+        if (doesJavaOverrideHaveIncompatibleValueParameterKinds(superDescriptor, subDescriptor)) {
+            return Result.INCOMPATIBLE
+        }
+
         return Result.UNKNOWN
     }
 
@@ -84,5 +92,53 @@ class JavaIncompatibilityRulesOverridabilityCondition : ExternalOverridabilityCo
         return true
     }
 
+
     override fun getContract() = ExternalOverridabilityCondition.Contract.CONFLICTS_ONLY
+
+    companion object {
+        /**
+         * Checks if any pair of corresponding value parameters has different type kinds, e.g. one is primitive and another is not
+         *
+         * As it comes from it's name it only checks overrides in Java classes
+         */
+        fun doesJavaOverrideHaveIncompatibleValueParameterKinds(
+                superDescriptor: CallableDescriptor,
+                subDescriptor: CallableDescriptor
+        ): Boolean {
+            if (subDescriptor !is JavaMethodDescriptor || superDescriptor !is FunctionDescriptor) return false
+            assert(subDescriptor.valueParameters.size == superDescriptor.valueParameters.size) {
+                "External overridability condition with CONFLICTS_ONLY should not be run with different value parameters size"
+            }
+
+            for ((subParameter, superParameter) in subDescriptor.original.valueParameters.zip(superDescriptor.original.valueParameters)) {
+                val isSubPrimitive = mapValueParameterType(subDescriptor, subParameter) is JvmType.Primitive
+                val isSuperPrimitive = mapValueParameterType(superDescriptor, superParameter) is JvmType.Primitive
+
+                if (isSubPrimitive != isSuperPrimitive) {
+                    return true
+                }
+            }
+
+            return false
+        }
+
+        private fun mapValueParameterType(f: FunctionDescriptor, valueParameterDescriptor: ValueParameterDescriptor) =
+                if (forceSingleValueParameterBoxing(f) || isPrimitiveCompareTo(f))
+                    valueParameterDescriptor.type.makeNullable().mapToJvmType()
+                else
+                    valueParameterDescriptor.type.mapToJvmType()
+
+        // It's useful here to suppose that 'Int.compareTo(Int)' requires boxing of it's value parameter
+        // As it happens in java.lang.Integer analogue
+        // It only affects additional built-ins loading (see 'testLoadBuiltIns' tests)
+        private fun isPrimitiveCompareTo(f: FunctionDescriptor): Boolean {
+            if (f.valueParameters.size != 1) return false
+            val classDescriptor =
+                    f.containingDeclaration as? ClassDescriptor ?: return false
+            val parameterClass =
+                    f.valueParameters.single().type.constructor.declarationDescriptor as? ClassDescriptor
+                    ?: return false
+            return KotlinBuiltIns.isPrimitiveClass(classDescriptor) && classDescriptor.fqNameSafe == parameterClass.fqNameSafe
+        }
+    }
 }
diff --git a/core/descriptor.loader.java/src/org/jetbrains/kotlin/load/java/lazy/descriptors/LazyJavaClassMemberScope.kt b/core/descriptor.loader.java/src/org/jetbrains/kotlin/load/java/lazy/descriptors/LazyJavaClassMemberScope.kt
index 6bf5848c755..10b680b0a71 100644
--- a/core/descriptor.loader.java/src/org/jetbrains/kotlin/load/java/lazy/descriptors/LazyJavaClassMemberScope.kt
+++ b/core/descriptor.loader.java/src/org/jetbrains/kotlin/load/java/lazy/descriptors/LazyJavaClassMemberScope.kt
@@ -49,6 +49,7 @@ import org.jetbrains.kotlin.load.java.typeEnhancement.enhanceSignatures
 import org.jetbrains.kotlin.name.Name
 import org.jetbrains.kotlin.resolve.DescriptorFactory
 import org.jetbrains.kotlin.resolve.DescriptorUtils
+import org.jetbrains.kotlin.resolve.ExternalOverridabilityCondition
 import org.jetbrains.kotlin.resolve.OverridingUtil
 import org.jetbrains.kotlin.resolve.scopes.DescriptorKindFilter
 import org.jetbrains.kotlin.serialization.deserialization.ErrorReporter
@@ -164,9 +165,12 @@ class LazyJavaClassMemberScope(
     }
 
     private fun CallableDescriptor.doesOverride(superDescriptor: CallableDescriptor): Boolean {
-        return OverridingUtil.DEFAULT.isOverridableByWithoutExternalConditions(
-                superDescriptor, this, /* checkReturnType = */ true
-        ).result == OverridingUtil.OverrideCompatibilityInfo.Result.OVERRIDABLE
+        val commonOverridabilityResult =
+                OverridingUtil.DEFAULT.isOverridableByWithoutExternalConditions(superDescriptor, this, true).result
+
+        return commonOverridabilityResult == OverridingUtil.OverrideCompatibilityInfo.Result.OVERRIDABLE &&
+                    !JavaIncompatibilityRulesOverridabilityCondition.doesJavaOverrideHaveIncompatibleValueParameterKinds(
+                            superDescriptor, this)
     }
 
     private fun PropertyDescriptor.findGetterOverride(
diff --git a/core/descriptor.loader.java/src/org/jetbrains/kotlin/load/kotlin/methodSignatureMapping.kt b/core/descriptor.loader.java/src/org/jetbrains/kotlin/load/kotlin/methodSignatureMapping.kt
index 0d8584d2130..79375f7dcf4 100644
--- a/core/descriptor.loader.java/src/org/jetbrains/kotlin/load/kotlin/methodSignatureMapping.kt
+++ b/core/descriptor.loader.java/src/org/jetbrains/kotlin/load/kotlin/methodSignatureMapping.kt
@@ -17,6 +17,8 @@
 package org.jetbrains.kotlin.load.kotlin
 
 import org.jetbrains.kotlin.descriptors.*
+import org.jetbrains.kotlin.load.java.BuiltinMethodsWithSpecialGenericSignature
+import org.jetbrains.kotlin.load.java.isFromJavaOrBuiltins
 import org.jetbrains.kotlin.name.ClassId
 import org.jetbrains.kotlin.platform.JavaToKotlinClassMap
 import org.jetbrains.kotlin.resolve.DescriptorUtils
@@ -44,6 +46,17 @@ fun FunctionDescriptor.computeJvmDescriptor()
             }
         }.toString()
 
+// Boxing is only necessary for 'remove(E): Boolean' of a MutableList<Int> implementation
+// Otherwise this method will clash with 'remove(I): E' also defined in the JDK interface (mapped to kotlin 'removeAt')
+fun forceSingleValueParameterBoxing(f: FunctionDescriptor): Boolean {
+    if (f.isFromJavaOrBuiltins()) return false
+
+    if (f.name.asString() != "remove" ||
+        (f.original.valueParameters.single().type.mapToJvmType() as? JvmType.Primitive)?.jvmPrimitiveType != JvmPrimitiveType.INT) return false
+
+    return BuiltinMethodsWithSpecialGenericSignature.getOverriddenBuiltinFunctionWithErasedValueParametersInJava(f) != null
+}
+
 // This method only returns not-null for class methods
 internal fun CallableDescriptor.computeJvmSignature(): String? = signatures {
     if (DescriptorUtils.isLocal(this@computeJvmSignature)) return null
@@ -72,16 +85,19 @@ internal val ClassId.internalName: String
     }
 
 private fun StringBuilder.appendErasedType(type: KotlinType) {
-    append(
-            JvmTypeFactoryImpl.toString(
-                    mapType(type, JvmTypeFactoryImpl, TypeMappingMode.DEFAULT, TypeMappingConfigurationImpl, descriptorTypeWriter = null)))
+    append(type.mapToJvmType())
 }
 
-private sealed class JvmType {
+internal fun KotlinType.mapToJvmType() =
+        mapType(this, JvmTypeFactoryImpl, TypeMappingMode.DEFAULT, TypeMappingConfigurationImpl, descriptorTypeWriter = null)
+
+sealed class JvmType {
     // null means 'void'
     class Primitive(val jvmPrimitiveType: JvmPrimitiveType?) : JvmType()
     class Object(val internalName: String) : JvmType()
     class Array(val elementType: JvmType) : JvmType()
+
+    override fun toString() = JvmTypeFactoryImpl.toString(this)
 }
 
 private object JvmTypeFactoryImpl : JvmTypeFactory<JvmType> {