diff --git a/compiler/testData/diagnostics/tests/platformTypes/commonSupertype/mixedElvis.kt b/compiler/testData/diagnostics/tests/platformTypes/commonSupertype/mixedElvis.kt
new file mode 100644
index 00000000000..a6f5329d0f4
--- /dev/null
+++ b/compiler/testData/diagnostics/tests/platformTypes/commonSupertype/mixedElvis.kt
@@ -0,0 +1,12 @@
+// !DIAGNOSTICS: -UNUSED_VARIABLE
+// !CHECK_TYPE
+
+import java.util.ArrayList
+
+fun foo(handlers: Array<MutableList<String>?>) {
+    val v = handlers[0] ?: ArrayList<String>()
+    handlers[0] = v
+    val js: MutableList<String> = v
+    v checkType { it : _<MutableList<String>>}
+    v checkType { it : _<MutableList<String?>>}
+}
\ No newline at end of file
diff --git a/compiler/testData/diagnostics/tests/platformTypes/commonSupertype/mixedElvis.txt b/compiler/testData/diagnostics/tests/platformTypes/commonSupertype/mixedElvis.txt
new file mode 100644
index 00000000000..1ee2d59f6da
--- /dev/null
+++ b/compiler/testData/diagnostics/tests/platformTypes/commonSupertype/mixedElvis.txt
@@ -0,0 +1,11 @@
+package
+
+internal fun foo(/*0*/ handlers: kotlin.Array<kotlin.MutableList<kotlin.String>?>): kotlin.Unit
+internal fun </*0*/ T> T.checkType(/*0*/ f: (_<T>) -> kotlin.Unit): (_<T>) -> kotlin.Unit
+
+internal final class _</*0*/ T> {
+    public constructor _</*0*/ T>()
+    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 open override /*1*/ /*fake_override*/ fun toString(): kotlin.String
+}
\ No newline at end of file
diff --git a/compiler/testData/diagnostics/tests/platformTypes/commonSupertype/mixedIf.kt b/compiler/testData/diagnostics/tests/platformTypes/commonSupertype/mixedIf.kt
new file mode 100644
index 00000000000..14f87fdfc59
--- /dev/null
+++ b/compiler/testData/diagnostics/tests/platformTypes/commonSupertype/mixedIf.kt
@@ -0,0 +1,20 @@
+// !DIAGNOSTICS: -UNUSED_VARIABLE
+// !CHECK_TYPE
+// FILE: p/J.java
+
+package p;
+
+public class J<G> {
+    public static J<String> j() { return null; }
+}
+
+// FILE: k.kt
+
+import p.*
+
+fun foo(j: J<String>) {
+    val v = if (true) j else J.j()
+    val js: J<String> = v
+    v checkType { it : _<J<String>>}
+    v checkType { it : _<J<String?>>}
+}
\ No newline at end of file
diff --git a/compiler/testData/diagnostics/tests/platformTypes/commonSupertype/mixedIf.txt b/compiler/testData/diagnostics/tests/platformTypes/commonSupertype/mixedIf.txt
new file mode 100644
index 00000000000..9f4886438da
--- /dev/null
+++ b/compiler/testData/diagnostics/tests/platformTypes/commonSupertype/mixedIf.txt
@@ -0,0 +1,11 @@
+package
+
+internal fun foo(/*0*/ j: p.J<kotlin.String>): kotlin.Unit
+internal fun </*0*/ T> T.checkType(/*0*/ f: (_<T>) -> kotlin.Unit): (_<T>) -> kotlin.Unit
+
+internal final class _</*0*/ T> {
+    public constructor _</*0*/ T>()
+    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 open override /*1*/ /*fake_override*/ fun toString(): kotlin.String
+}
\ No newline at end of file
diff --git a/compiler/testData/diagnostics/tests/platformTypes/commonSupertype/withNothing.kt b/compiler/testData/diagnostics/tests/platformTypes/commonSupertype/withNothing.kt
new file mode 100644
index 00000000000..71fcbb0ea12
--- /dev/null
+++ b/compiler/testData/diagnostics/tests/platformTypes/commonSupertype/withNothing.kt
@@ -0,0 +1,24 @@
+// !DIAGNOSTICS: -UNUSED_PARAMETER
+// !CHECK_TYPE
+// FILE: p/J.java
+
+package p;
+
+public class J {
+    public static J j() { return null; }
+}
+
+// FILE: k.kt
+
+import p.*
+
+trait Out<out T1>
+
+fun <T> f(a: Out<T>, b: Out<T>, c: Out<T>): T = null!!
+fun <T> out(t: T): Out<MutableList<T>> = null!!
+
+fun test(a: Out<Nothing>, b: Out<MutableList<J>>) {
+    val v = f(a, b, out(J.j()))
+    v checkType { it : _<MutableList<J>>}
+    v checkType { it : _<MutableList<J?>>}
+}
\ No newline at end of file
diff --git a/compiler/testData/diagnostics/tests/platformTypes/commonSupertype/withNothing.txt b/compiler/testData/diagnostics/tests/platformTypes/commonSupertype/withNothing.txt
new file mode 100644
index 00000000000..69d16eef60f
--- /dev/null
+++ b/compiler/testData/diagnostics/tests/platformTypes/commonSupertype/withNothing.txt
@@ -0,0 +1,19 @@
+package
+
+internal fun </*0*/ T> f(/*0*/ a: Out<T>, /*1*/ b: Out<T>, /*2*/ c: Out<T>): T
+internal fun </*0*/ T> out(/*0*/ t: T): Out<kotlin.MutableList<T>>
+internal fun test(/*0*/ a: Out<kotlin.Nothing>, /*1*/ b: Out<kotlin.MutableList<p.J>>): kotlin.Unit
+internal fun </*0*/ T> T.checkType(/*0*/ f: (_<T>) -> kotlin.Unit): (_<T>) -> kotlin.Unit
+
+internal trait Out</*0*/ out T1> {
+    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 open override /*1*/ /*fake_override*/ fun toString(): kotlin.String
+}
+
+internal final class _</*0*/ T> {
+    public constructor _</*0*/ T>()
+    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 open override /*1*/ /*fake_override*/ fun toString(): kotlin.String
+}
\ No newline at end of file
diff --git a/compiler/testData/diagnostics/tests/platformTypes/methodCall/multipleExactBounds.kt b/compiler/testData/diagnostics/tests/platformTypes/methodCall/multipleExactBounds.kt
new file mode 100644
index 00000000000..084ea2b60ca
--- /dev/null
+++ b/compiler/testData/diagnostics/tests/platformTypes/methodCall/multipleExactBounds.kt
@@ -0,0 +1,21 @@
+import java.util.HashMap
+
+trait ModuleDescriptorImpl
+trait ModuleInfo
+trait ResolverForModule
+trait ResolverForProject<M1, R1>
+
+class ResolverForProjectImpl<M : ModuleInfo, R : ResolverForModule>(
+        descriptorByModule: Map<M, ModuleDescriptorImpl>,
+        delegateResolver: ResolverForProject<M, R>
+) : ResolverForProject<M, R>
+
+fun <M2: ModuleInfo, A: ResolverForModule> foo(delegateResolver: ResolverForProject<M2, A>): ResolverForProject<M2, A> {
+    val descriptorByModule = HashMap<M2, ModuleDescriptorImpl>()
+    return ResolverForProjectImpl(descriptorByModule, delegateResolver)
+}
+
+// M = M2
+// HashMap<M2, MDI> :< Map<M, MDI> => M = M2!
+// R = A
+// RFP<M2, A> :< RFP<M, R>
\ No newline at end of file
diff --git a/compiler/testData/diagnostics/tests/platformTypes/methodCall/multipleExactBounds.txt b/compiler/testData/diagnostics/tests/platformTypes/methodCall/multipleExactBounds.txt
new file mode 100644
index 00000000000..916ef884014
--- /dev/null
+++ b/compiler/testData/diagnostics/tests/platformTypes/methodCall/multipleExactBounds.txt
@@ -0,0 +1,34 @@
+package
+
+internal fun </*0*/ M2 : ModuleInfo, /*1*/ A : ResolverForModule> foo(/*0*/ delegateResolver: ResolverForProject<M2, A>): ResolverForProject<M2, A>
+
+internal trait ModuleDescriptorImpl {
+    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 open override /*1*/ /*fake_override*/ fun toString(): kotlin.String
+}
+
+internal trait ModuleInfo {
+    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 open override /*1*/ /*fake_override*/ fun toString(): kotlin.String
+}
+
+internal trait ResolverForModule {
+    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 open override /*1*/ /*fake_override*/ fun toString(): kotlin.String
+}
+
+internal trait ResolverForProject</*0*/ M1, /*1*/ R1> {
+    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 open override /*1*/ /*fake_override*/ fun toString(): kotlin.String
+}
+
+internal final class ResolverForProjectImpl</*0*/ M : ModuleInfo, /*1*/ R : ResolverForModule> : ResolverForProject<M, R> {
+    public constructor ResolverForProjectImpl</*0*/ M : ModuleInfo, /*1*/ R : ResolverForModule>(/*0*/ descriptorByModule: kotlin.Map<M, ModuleDescriptorImpl>, /*1*/ delegateResolver: ResolverForProject<M, R>)
+    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 open override /*1*/ /*fake_override*/ fun toString(): kotlin.String
+}
\ No newline at end of file
diff --git a/compiler/testData/diagnostics/tests/platformTypes/methodCall/multipleExactBoundsNullable.kt b/compiler/testData/diagnostics/tests/platformTypes/methodCall/multipleExactBoundsNullable.kt
new file mode 100644
index 00000000000..2ad7f1cb09b
--- /dev/null
+++ b/compiler/testData/diagnostics/tests/platformTypes/methodCall/multipleExactBoundsNullable.kt
@@ -0,0 +1,26 @@
+import java.util.HashMap
+
+trait ResolverForProject<M1> {
+    val exposeM: M1 get() = null!!
+}
+
+class ResolverForProjectImpl<M>(
+        descriptorByModule: Map<M, String>,
+        delegateResolver: ResolverForProject<M>
+) : ResolverForProject<M>
+
+trait WithFoo {
+    fun foo()
+}
+
+fun <M2: WithFoo> foo(delegateResolver: ResolverForProject<M2?>): ResolverForProject<M2> {
+    val descriptorByModule = HashMap<M2, String>()
+    val result = ResolverForProjectImpl(descriptorByModule, delegateResolver)
+    result.exposeM.foo() // M is not M2?
+    result.exposeM?.foo() // no warning, M is not M2, hense M is M2!
+
+    return ResolverForProjectImpl(descriptorByModule, delegateResolver) // another bound check
+}
+
+// HashMap<M2, String> :< Map<M, String> => M = M2!
+// RFP<M2?> :< RFP<M> => M = M2?
\ No newline at end of file
diff --git a/compiler/testData/diagnostics/tests/platformTypes/methodCall/multipleExactBoundsNullable.txt b/compiler/testData/diagnostics/tests/platformTypes/methodCall/multipleExactBoundsNullable.txt
new file mode 100644
index 00000000000..9fee42620c3
--- /dev/null
+++ b/compiler/testData/diagnostics/tests/platformTypes/methodCall/multipleExactBoundsNullable.txt
@@ -0,0 +1,25 @@
+package
+
+internal fun </*0*/ M2 : WithFoo> foo(/*0*/ delegateResolver: ResolverForProject<M2?>): ResolverForProject<M2>
+
+internal trait ResolverForProject</*0*/ M1> {
+    internal open val exposeM: M1
+    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 open override /*1*/ /*fake_override*/ fun toString(): kotlin.String
+}
+
+internal final class ResolverForProjectImpl</*0*/ M> : ResolverForProject<M> {
+    public constructor ResolverForProjectImpl</*0*/ M>(/*0*/ descriptorByModule: kotlin.Map<M, kotlin.String>, /*1*/ delegateResolver: ResolverForProject<M>)
+    internal open override /*1*/ /*fake_override*/ val exposeM: M
+    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 open override /*1*/ /*fake_override*/ fun toString(): kotlin.String
+}
+
+internal trait WithFoo {
+    public open override /*1*/ /*fake_override*/ fun equals(/*0*/ other: kotlin.Any?): kotlin.Boolean
+    internal abstract fun foo(): 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/tests/org/jetbrains/jet/checkers/JetDiagnosticsTestGenerated.java b/compiler/tests/org/jetbrains/jet/checkers/JetDiagnosticsTestGenerated.java
index 33bdbdc3df0..e732cf35eda 100644
--- a/compiler/tests/org/jetbrains/jet/checkers/JetDiagnosticsTestGenerated.java
+++ b/compiler/tests/org/jetbrains/jet/checkers/JetDiagnosticsTestGenerated.java
@@ -7793,6 +7793,18 @@ public class JetDiagnosticsTestGenerated extends AbstractJetDiagnosticsTest {
                     doTest(fileName);
                 }
                 
+                @TestMetadata("mixedElvis.kt")
+                public void testMixedElvis() throws Exception {
+                    String fileName = JetTestUtils.navigationMetadata("compiler/testData/diagnostics/tests/platformTypes/commonSupertype/mixedElvis.kt");
+                    doTest(fileName);
+                }
+                
+                @TestMetadata("mixedIf.kt")
+                public void testMixedIf() throws Exception {
+                    String fileName = JetTestUtils.navigationMetadata("compiler/testData/diagnostics/tests/platformTypes/commonSupertype/mixedIf.kt");
+                    doTest(fileName);
+                }
+                
                 @TestMetadata("recursiveGeneric.kt")
                 public void testRecursiveGeneric() throws Exception {
                     String fileName = JetTestUtils.navigationMetadata("compiler/testData/diagnostics/tests/platformTypes/commonSupertype/recursiveGeneric.kt");
@@ -7811,6 +7823,12 @@ public class JetDiagnosticsTestGenerated extends AbstractJetDiagnosticsTest {
                     doTest(fileName);
                 }
                 
+                @TestMetadata("withNothing.kt")
+                public void testWithNothing() throws Exception {
+                    String fileName = JetTestUtils.navigationMetadata("compiler/testData/diagnostics/tests/platformTypes/commonSupertype/withNothing.kt");
+                    doTest(fileName);
+                }
+                
             }
             
             @TestMetadata("compiler/testData/diagnostics/tests/platformTypes/methodCall")
@@ -7869,6 +7887,18 @@ public class JetDiagnosticsTestGenerated extends AbstractJetDiagnosticsTest {
                     doTest(fileName);
                 }
                 
+                @TestMetadata("multipleExactBounds.kt")
+                public void testMultipleExactBounds() throws Exception {
+                    String fileName = JetTestUtils.navigationMetadata("compiler/testData/diagnostics/tests/platformTypes/methodCall/multipleExactBounds.kt");
+                    doTest(fileName);
+                }
+                
+                @TestMetadata("multipleExactBoundsNullable.kt")
+                public void testMultipleExactBoundsNullable() throws Exception {
+                    String fileName = JetTestUtils.navigationMetadata("compiler/testData/diagnostics/tests/platformTypes/methodCall/multipleExactBoundsNullable.kt");
+                    doTest(fileName);
+                }
+                
                 @TestMetadata("objectArray.kt")
                 public void testObjectArray() throws Exception {
                     String fileName = JetTestUtils.navigationMetadata("compiler/testData/diagnostics/tests/platformTypes/methodCall/objectArray.kt");
diff --git a/core/descriptors/src/org/jetbrains/jet/lang/resolve/calls/inference/TypeBoundsImpl.java b/core/descriptors/src/org/jetbrains/jet/lang/resolve/calls/inference/TypeBoundsImpl.java
index 33894abd35e..57a3580048a 100644
--- a/core/descriptors/src/org/jetbrains/jet/lang/resolve/calls/inference/TypeBoundsImpl.java
+++ b/core/descriptors/src/org/jetbrains/jet/lang/resolve/calls/inference/TypeBoundsImpl.java
@@ -156,10 +156,10 @@ public class TypeBoundsImpl implements TypeBounds {
         }
 
         Set<JetType> exactBounds = filterBounds(bounds, BoundKind.EXACT_BOUND, values);
-        if (exactBounds.size() == 1) {
-            JetType exactBound = exactBounds.iterator().next();
-            if (tryPossibleAnswer(exactBound)) {
-                return Collections.singleton(exactBound);
+        JetType bestFit = TypesPackage.singleBestRepresentative(exactBounds);
+        if (bestFit != null) {
+            if (tryPossibleAnswer(bestFit)) {
+                return Collections.singleton(bestFit);
             }
         }
         values.addAll(exactBounds);
diff --git a/core/descriptors/src/org/jetbrains/jet/lang/types/CommonSupertypes.java b/core/descriptors/src/org/jetbrains/jet/lang/types/CommonSupertypes.java
index 5b7e7cbcfde..d0208d8c735 100644
--- a/core/descriptors/src/org/jetbrains/jet/lang/types/CommonSupertypes.java
+++ b/core/descriptors/src/org/jetbrains/jet/lang/types/CommonSupertypes.java
@@ -103,7 +103,9 @@ public class CommonSupertypes {
     private static JetType commonSuperTypeForInflexible(@NotNull Collection<JetType> types, int recursionDepth, int maxDepth) {
         assert !types.isEmpty();
         Collection<JetType> typeSet = new HashSet<JetType>(types);
-        if (typeSet.size() == 1) return typeSet.iterator().next();
+
+        JetType bestFit = TypesPackage.singleBestRepresentative(typeSet);
+        if (bestFit != null) return bestFit;
 
         // If any of the types is nullable, the result must be nullable
         // This also removed Nothing and Nothing? because they are subtypes of everything else
@@ -232,8 +234,9 @@ public class CommonSupertypes {
             @NotNull Set<TypeProjection> typeProjections,
             int recursionDepth, int maxDepth
     ) {
-        if (typeProjections.size() == 1) {
-            return typeProjections.iterator().next();
+        TypeProjection singleBestProjection = TypesPackage.singleBestRepresentative(typeProjections);
+        if (singleBestProjection != null) {
+            return singleBestProjection;
         }
 
         if (recursionDepth >= maxDepth) {
diff --git a/core/descriptors/src/org/jetbrains/jet/lang/types/flexibleTypes.kt b/core/descriptors/src/org/jetbrains/jet/lang/types/flexibleTypes.kt
index b218a9cdb6c..93d90326a0e 100644
--- a/core/descriptors/src/org/jetbrains/jet/lang/types/flexibleTypes.kt
+++ b/core/descriptors/src/org/jetbrains/jet/lang/types/flexibleTypes.kt
@@ -18,6 +18,7 @@ package org.jetbrains.jet.lang.types
 
 import org.jetbrains.jet.lang.types.checker.JetTypeChecker
 import org.jetbrains.jet.lang.types.Approximation.DataFlowExtras
+import org.jetbrains.kotlin.util.printAndReturn
 
 public trait Flexibility : TypeCapability {
     // lowerBound is a subtype of upperBound
@@ -29,6 +30,38 @@ public trait Flexibility : TypeCapability {
 public fun JetType.isFlexible(): Boolean = this.getCapability(javaClass<Flexibility>()) != null
 public fun JetType.flexibility(): Flexibility = this.getCapability(javaClass<Flexibility>())!!
 
+// This function is intended primarily for sets: since JetType.equals() represents _syntactical_ equality of types,
+// whereas JetTypeChecker.DEFAULT.equalsTypes() represents semantical equality
+// A set of types (e.g. exact bounds etc) may contain, for example, X, X? and X!
+// These are not equal syntactically (by JetType.equals()), but X! is _compatible_ with others as exact bounds,
+// moreover, X! is a better fit.
+//
+// So, we are looking for a type among this set such that it is equal to all others semantically
+// (by JetTypeChecker.DEFAULT.equalsTypes()), and fits at least as well as they do.
+fun Collection<JetType>.singleBestRepresentative(): JetType? {
+    if (this.size() == 1) return this.first()
+
+    return this.firstOrNull {
+        candidate ->
+        this.all {
+            other ->
+            candidate == other || JetTypeChecker.DEFAULT.equalTypes(candidate, other)
+        }
+    }
+}
+
+fun Collection<TypeProjection>.singleBestRepresentative(): TypeProjection? {
+    if (this.size() == 1) return this.first()
+
+    val projectionKinds = this.map { it.getProjectionKind() }.toSet()
+    if (projectionKinds.size() != 1) return null
+
+    val bestType = this.map { it.getType() }.singleBestRepresentative()
+    if (bestType == null) return null
+
+    return TypeProjectionImpl(projectionKinds.single(), bestType)
+}
+
 public fun JetType.lowerIfFlexible(): JetType = if (this.isFlexible()) this.flexibility().getLowerBound() else this
 public fun JetType.upperIfFlexible(): JetType = if (this.isFlexible()) this.flexibility().getUpperBound() else this