diff --git a/idea/ide-common/src/org/jetbrains/kotlin/idea/util/TypeUtils.kt b/idea/ide-common/src/org/jetbrains/kotlin/idea/util/TypeUtils.kt
index 02cd24a3a3a..ab552c830ba 100644
--- a/idea/ide-common/src/org/jetbrains/kotlin/idea/util/TypeUtils.kt
+++ b/idea/ide-common/src/org/jetbrains/kotlin/idea/util/TypeUtils.kt
@@ -18,7 +18,10 @@
 
 package org.jetbrains.kotlin.idea.util
 
+import org.jetbrains.kotlin.builtins.getReturnTypeFromFunctionType
+import org.jetbrains.kotlin.builtins.isBuiltinFunctionalType
 import org.jetbrains.kotlin.builtins.jvm.JavaToKotlinClassMap
+import org.jetbrains.kotlin.builtins.replaceReturnType
 import org.jetbrains.kotlin.descriptors.ClassDescriptor
 import org.jetbrains.kotlin.descriptors.Modality
 import org.jetbrains.kotlin.descriptors.TypeParameterDescriptor
@@ -124,35 +127,70 @@ fun KotlinType.getResolvableApproximations(
 ): Sequence<KotlinType> {
     return (listOf(this) + TypeUtils.getAllSupertypes(this))
         .asSequence()
-        .filter { it.isResolvableInScope(scope, checkTypeParameters, allowIntersections) }
-        .mapNotNull mapArgs@{
-            val resolvableArgs = it.arguments.filterTo(SmartSet.create()) { typeProjection ->
-                typeProjection.type.isResolvableInScope(
-                    scope,
-                    checkTypeParameters
-                )
-            }
-            if (resolvableArgs.containsAll(it.arguments)) return@mapArgs it
-
-            val newArguments = (it.arguments zip it.constructor.parameters).map { pair ->
-                val (arg, param) = pair
-                when {
-                    arg in resolvableArgs -> arg
-
-                    arg.projectionKind == Variance.OUT_VARIANCE ||
-                            param.variance == Variance.OUT_VARIANCE -> TypeProjectionImpl(
-                        arg.projectionKind,
-                        arg.type.approximateWithResolvableType(scope, checkTypeParameters)
-                    )
-
-                    else -> return@mapArgs null
-                }
-            }
-
-            it.replace(newArguments)
+        .mapNotNull {
+            it.asTypeProjection()
+                .fixTypeProjection(scope, checkTypeParameters, allowIntersections, isOutVariance = true)
+                ?.type
         }
 }
 
+private fun TypeProjection.fixTypeProjection(
+    scope: LexicalScope?,
+    checkTypeParameters: Boolean,
+    allowIntersections: Boolean,
+    isOutVariance: Boolean
+): TypeProjection? {
+    if (!type.isResolvableInScope(scope, checkTypeParameters, allowIntersections)) return null
+    if (type.arguments.isEmpty()) return this
+
+    val resolvableArgs = type.arguments.filterTo(SmartSet.create()) { typeProjection ->
+        typeProjection.type.isResolvableInScope(scope, checkTypeParameters, allowIntersections)
+    }
+
+    if (resolvableArgs.containsAll(type.arguments)) {
+        fun fixArguments(type: KotlinType): KotlinType? = type.replace(
+            (type.arguments zip type.constructor.parameters).map { (arg, param) ->
+                if (arg.isStarProjection) arg
+                else arg.fixTypeProjection(
+                    scope,
+                    checkTypeParameters,
+                    allowIntersections,
+                    isOutVariance = isOutVariance && param.variance == Variance.OUT_VARIANCE
+                ) ?: when {
+                    !isOutVariance -> return null
+                    param.variance == Variance.OUT_VARIANCE -> arg.type.approximateWithResolvableType(
+                        scope,
+                        checkTypeParameters
+                    ).asTypeProjection()
+                    else -> type.replaceArgumentsWithStarProjections().arguments.first()
+                }
+            })
+
+        return if (type.isBuiltinFunctionalType) {
+            val returnType = type.getReturnTypeFromFunctionType()
+            type.replaceReturnType(fixArguments(returnType) ?: return null).asTypeProjection()
+        } else fixArguments(type)?.asTypeProjection()
+    }
+
+    if (!isOutVariance) return null
+
+    val newArguments = (type.arguments zip type.constructor.parameters).map { (arg, param) ->
+        when {
+            arg in resolvableArgs -> arg
+
+            arg.projectionKind == Variance.OUT_VARIANCE ||
+                    param.variance == Variance.OUT_VARIANCE -> TypeProjectionImpl(
+                arg.projectionKind,
+                arg.type.approximateWithResolvableType(scope, checkTypeParameters)
+            )
+
+            else -> return if (isOutVariance) type.replaceArgumentsWithStarProjections().asTypeProjection() else null
+        }
+    }
+
+    return type.replace(newArguments).asTypeProjection()
+}
+
 fun KotlinType.isAbstract(): Boolean {
     val modality = (constructor.declarationDescriptor as? ClassDescriptor)?.modality
     return modality == Modality.ABSTRACT || modality == Modality.SEALED
diff --git a/idea/src/org/jetbrains/kotlin/idea/intentions/SpecifyTypeExplicitlyIntention.kt b/idea/src/org/jetbrains/kotlin/idea/intentions/SpecifyTypeExplicitlyIntention.kt
index fa67e3cb4e6..826a9d9cd96 100644
--- a/idea/src/org/jetbrains/kotlin/idea/intentions/SpecifyTypeExplicitlyIntention.kt
+++ b/idea/src/org/jetbrains/kotlin/idea/intentions/SpecifyTypeExplicitlyIntention.kt
@@ -26,9 +26,7 @@ import com.intellij.psi.PsiComment
 import com.intellij.psi.PsiDocumentManager
 import org.jetbrains.kotlin.builtins.KotlinBuiltIns
 import org.jetbrains.kotlin.descriptors.CallableDescriptor
-import org.jetbrains.kotlin.descriptors.FunctionDescriptor
 import org.jetbrains.kotlin.descriptors.PropertyDescriptor
-import org.jetbrains.kotlin.descriptors.TypeParameterDescriptor
 import org.jetbrains.kotlin.idea.caches.resolve.getResolutionFacade
 import org.jetbrains.kotlin.idea.caches.resolve.resolveToDescriptorIfAny
 import org.jetbrains.kotlin.idea.core.ShortenReferences
@@ -131,17 +129,8 @@ class SpecifyTypeExplicitlyIntention : SelfTargetingRangeIntention<KtCallableDec
             val bindingContext = resolutionFacade.analyze(contextElement, BodyResolveMode.PARTIAL)
             val scope = contextElement.getResolutionScope(bindingContext, resolutionFacade)
 
-            var checkTypeParameters = true
-            val descriptor = exprType.constructor.declarationDescriptor
-            if (descriptor != null && descriptor is TypeParameterDescriptor) {
-                val owner = descriptor.containingDeclaration
-                if (owner is FunctionDescriptor && owner.typeParameters.contains(descriptor)) {
-                    checkTypeParameters = false
-                }
-            }
-
             fun KotlinType.toResolvableApproximations(): List<KotlinType> =
-                with(getResolvableApproximations(scope, checkTypeParameters).toList()) {
+                with(getResolvableApproximations(scope, checkTypeParameters = false).toList()) {
                     when {
                         exprType.isNullabilityFlexible() -> flatMap {
                             listOf(TypeUtils.makeNotNullable(it), TypeUtils.makeNullable(it))
diff --git a/idea/testData/intentions/specifyTypeExplicitly/genericClassWithTypeParameters.kt b/idea/testData/intentions/specifyTypeExplicitly/genericClassWithTypeParameters.kt
new file mode 100644
index 00000000000..1cc185a9a87
--- /dev/null
+++ b/idea/testData/intentions/specifyTypeExplicitly/genericClassWithTypeParameters.kt
@@ -0,0 +1,5 @@
+// WITH_RUNTIME
+inline fun <reified T> foo<caret>() = of(T::class.java)
+
+class Foo<F>
+fun <F> of(c: Class<F>): Foo<Foo<F>> = Foo()
\ No newline at end of file
diff --git a/idea/testData/intentions/specifyTypeExplicitly/genericClassWithTypeParameters.kt.after b/idea/testData/intentions/specifyTypeExplicitly/genericClassWithTypeParameters.kt.after
new file mode 100644
index 00000000000..fb1306f78d8
--- /dev/null
+++ b/idea/testData/intentions/specifyTypeExplicitly/genericClassWithTypeParameters.kt.after
@@ -0,0 +1,5 @@
+// WITH_RUNTIME
+inline fun <reified T> foo(): Foo<Foo<T>> = of(T::class.java)
+
+class Foo<F>
+fun <F> of(c: Class<F>): Foo<Foo<F>> = Foo()
\ No newline at end of file
diff --git a/idea/testData/intentions/specifyTypeExplicitly/genericClassWithTypeParameters2.kt b/idea/testData/intentions/specifyTypeExplicitly/genericClassWithTypeParameters2.kt
new file mode 100644
index 00000000000..65cf79255ed
--- /dev/null
+++ b/idea/testData/intentions/specifyTypeExplicitly/genericClassWithTypeParameters2.kt
@@ -0,0 +1,5 @@
+// WITH_RUNTIME
+inline fun <reified T> foo<caret>() = of(T::class.java)
+
+class Foo<F>
+fun <F> of(c: Class<F>): Foo<F> = Foo()
\ No newline at end of file
diff --git a/idea/testData/intentions/specifyTypeExplicitly/genericClassWithTypeParameters2.kt.after b/idea/testData/intentions/specifyTypeExplicitly/genericClassWithTypeParameters2.kt.after
new file mode 100644
index 00000000000..0af3434bfba
--- /dev/null
+++ b/idea/testData/intentions/specifyTypeExplicitly/genericClassWithTypeParameters2.kt.after
@@ -0,0 +1,5 @@
+// WITH_RUNTIME
+inline fun <reified T> foo(): Foo<T> = of(T::class.java)
+
+class Foo<F>
+fun <F> of(c: Class<F>): Foo<F> = Foo()
\ No newline at end of file
diff --git a/idea/testData/intentions/specifyTypeExplicitly/innerTypeParameter.kt b/idea/testData/intentions/specifyTypeExplicitly/innerTypeParameter.kt
new file mode 100644
index 00000000000..3bda45ef53c
--- /dev/null
+++ b/idea/testData/intentions/specifyTypeExplicitly/innerTypeParameter.kt
@@ -0,0 +1,9 @@
+class A<T>
+class B<T>
+class C<T>
+class D<K, V>
+class E
+private fun test()<caret> = {
+    class Local
+    C<D<A<Local>, B<D<Local, A<E>>>>>()
+}
\ No newline at end of file
diff --git a/idea/testData/intentions/specifyTypeExplicitly/innerTypeParameter.kt.after b/idea/testData/intentions/specifyTypeExplicitly/innerTypeParameter.kt.after
new file mode 100644
index 00000000000..54f24b98afe
--- /dev/null
+++ b/idea/testData/intentions/specifyTypeExplicitly/innerTypeParameter.kt.after
@@ -0,0 +1,9 @@
+class A<T>
+class B<T>
+class C<T>
+class D<K, V>
+class E
+private fun test(): () -> C<*> = {
+    class Local
+    C<D<A<Local>, B<D<Local, A<E>>>>>()
+}
\ No newline at end of file
diff --git a/idea/testData/intentions/specifyTypeExplicitly/innerTypeParameter2.kt b/idea/testData/intentions/specifyTypeExplicitly/innerTypeParameter2.kt
new file mode 100644
index 00000000000..e9dbbb12133
--- /dev/null
+++ b/idea/testData/intentions/specifyTypeExplicitly/innerTypeParameter2.kt
@@ -0,0 +1,8 @@
+class A<T>
+class B<T>
+class C<T>
+class D<K, V>
+class E
+private fun test()<caret> = {
+    C<D<A<E>, B<D<C<E>, A<E>>>>>()
+}
\ No newline at end of file
diff --git a/idea/testData/intentions/specifyTypeExplicitly/innerTypeParameter2.kt.after b/idea/testData/intentions/specifyTypeExplicitly/innerTypeParameter2.kt.after
new file mode 100644
index 00000000000..3c4afd1fce2
--- /dev/null
+++ b/idea/testData/intentions/specifyTypeExplicitly/innerTypeParameter2.kt.after
@@ -0,0 +1,8 @@
+class A<T>
+class B<T>
+class C<T>
+class D<K, V>
+class E
+private fun test(): () -> C<D<A<E>, B<D<C<E>, A<E>>>>> = {
+    C<D<A<E>, B<D<C<E>, A<E>>>>>()
+}
\ No newline at end of file
diff --git a/idea/testData/intentions/specifyTypeExplicitly/localClassInSecondTypeParameter.kt b/idea/testData/intentions/specifyTypeExplicitly/localClassInSecondTypeParameter.kt
new file mode 100644
index 00000000000..053a69837e2
--- /dev/null
+++ b/idea/testData/intentions/specifyTypeExplicitly/localClassInSecondTypeParameter.kt
@@ -0,0 +1,6 @@
+class F
+class TestClass<V, K>
+private fun test()<caret> = {
+    class Local
+    TestClass<F, Local>()
+}
\ No newline at end of file
diff --git a/idea/testData/intentions/specifyTypeExplicitly/localClassInSecondTypeParameter.kt.after b/idea/testData/intentions/specifyTypeExplicitly/localClassInSecondTypeParameter.kt.after
new file mode 100644
index 00000000000..0a34e57241e
--- /dev/null
+++ b/idea/testData/intentions/specifyTypeExplicitly/localClassInSecondTypeParameter.kt.after
@@ -0,0 +1,6 @@
+class F
+class TestClass<V, K>
+private fun test(): () -> TestClass<F, *> = {
+    class Local
+    TestClass<F, Local>()
+}
\ No newline at end of file
diff --git a/idea/testData/intentions/specifyTypeExplicitly/localClassInSecondTypeParameter2.kt b/idea/testData/intentions/specifyTypeExplicitly/localClassInSecondTypeParameter2.kt
new file mode 100644
index 00000000000..c16e81425de
--- /dev/null
+++ b/idea/testData/intentions/specifyTypeExplicitly/localClassInSecondTypeParameter2.kt
@@ -0,0 +1,7 @@
+open class F
+class TestClass<V, out K>
+
+private fun test()<caret> = {
+    class Local : F()
+    TestClass<F, Local>()
+}
\ No newline at end of file
diff --git a/idea/testData/intentions/specifyTypeExplicitly/localClassInSecondTypeParameter2.kt.after b/idea/testData/intentions/specifyTypeExplicitly/localClassInSecondTypeParameter2.kt.after
new file mode 100644
index 00000000000..b733d747b95
--- /dev/null
+++ b/idea/testData/intentions/specifyTypeExplicitly/localClassInSecondTypeParameter2.kt.after
@@ -0,0 +1,7 @@
+open class F
+class TestClass<V, out K>
+
+private fun test(): () -> TestClass<F, F> = {
+    class Local : F()
+    TestClass<F, Local>()
+}
\ No newline at end of file
diff --git a/idea/testData/intentions/specifyTypeExplicitly/localClassInSecondTypeParameter3.kt b/idea/testData/intentions/specifyTypeExplicitly/localClassInSecondTypeParameter3.kt
new file mode 100644
index 00000000000..b3464b8aa46
--- /dev/null
+++ b/idea/testData/intentions/specifyTypeExplicitly/localClassInSecondTypeParameter3.kt
@@ -0,0 +1,7 @@
+open class F
+class TestClass<V, out K>
+
+private fun test()<caret> = {
+    class Local
+    TestClass<F, Local?>()
+}
\ No newline at end of file
diff --git a/idea/testData/intentions/specifyTypeExplicitly/localClassInSecondTypeParameter3.kt.after b/idea/testData/intentions/specifyTypeExplicitly/localClassInSecondTypeParameter3.kt.after
new file mode 100644
index 00000000000..40da2097f01
--- /dev/null
+++ b/idea/testData/intentions/specifyTypeExplicitly/localClassInSecondTypeParameter3.kt.after
@@ -0,0 +1,7 @@
+open class F
+class TestClass<V, out K>
+
+private fun test(): () -> TestClass<F, Any?> = {
+    class Local
+    TestClass<F, Local?>()
+}
\ No newline at end of file
diff --git a/idea/testData/intentions/specifyTypeExplicitly/localClassInTypeParameter.kt b/idea/testData/intentions/specifyTypeExplicitly/localClassInTypeParameter.kt
new file mode 100644
index 00000000000..f55e1997aa1
--- /dev/null
+++ b/idea/testData/intentions/specifyTypeExplicitly/localClassInTypeParameter.kt
@@ -0,0 +1,5 @@
+class TestClass<T>
+private fun test()<caret> = {
+    class Local
+    TestClass<Local>()
+}
\ No newline at end of file
diff --git a/idea/testData/intentions/specifyTypeExplicitly/localClassInTypeParameter.kt.after b/idea/testData/intentions/specifyTypeExplicitly/localClassInTypeParameter.kt.after
new file mode 100644
index 00000000000..5b06d1eed5c
--- /dev/null
+++ b/idea/testData/intentions/specifyTypeExplicitly/localClassInTypeParameter.kt.after
@@ -0,0 +1,5 @@
+class TestClass<T>
+private fun test(): () -> TestClass<*> = {
+    class Local
+    TestClass<Local>()
+}
\ No newline at end of file
diff --git a/idea/testData/intentions/specifyTypeExplicitly/outClass.kt b/idea/testData/intentions/specifyTypeExplicitly/outClass.kt
new file mode 100644
index 00000000000..5e44b395e73
--- /dev/null
+++ b/idea/testData/intentions/specifyTypeExplicitly/outClass.kt
@@ -0,0 +1,8 @@
+open class F
+class B<out T>
+class K<out T>
+
+private fun check()<caret> = {
+    class Local : F()
+    B<K<Local>>()
+}
\ No newline at end of file
diff --git a/idea/testData/intentions/specifyTypeExplicitly/outClass.kt.after b/idea/testData/intentions/specifyTypeExplicitly/outClass.kt.after
new file mode 100644
index 00000000000..7c1dd82390e
--- /dev/null
+++ b/idea/testData/intentions/specifyTypeExplicitly/outClass.kt.after
@@ -0,0 +1,8 @@
+open class F
+class B<out T>
+class K<out T>
+
+private fun check(): () -> B<K<F>> = {
+    class Local : F()
+    B<K<Local>>()
+}
\ No newline at end of file
diff --git a/idea/testData/intentions/specifyTypeExplicitly/outClass2.kt b/idea/testData/intentions/specifyTypeExplicitly/outClass2.kt
new file mode 100644
index 00000000000..3d3d93f32a2
--- /dev/null
+++ b/idea/testData/intentions/specifyTypeExplicitly/outClass2.kt
@@ -0,0 +1,8 @@
+open class F
+class B<out T>
+class K<T>
+
+private fun check()<caret> = {
+    class Local : F()
+    B<K<Local>>()
+}
\ No newline at end of file
diff --git a/idea/testData/intentions/specifyTypeExplicitly/outClass2.kt.after b/idea/testData/intentions/specifyTypeExplicitly/outClass2.kt.after
new file mode 100644
index 00000000000..40792c6bcbd
--- /dev/null
+++ b/idea/testData/intentions/specifyTypeExplicitly/outClass2.kt.after
@@ -0,0 +1,8 @@
+open class F
+class B<out T>
+class K<T>
+
+private fun check(): () -> B<K<*>> = {
+    class Local : F()
+    B<K<Local>>()
+}
\ No newline at end of file
diff --git a/idea/testData/intentions/specifyTypeExplicitly/outClass3.kt b/idea/testData/intentions/specifyTypeExplicitly/outClass3.kt
new file mode 100644
index 00000000000..1ea42c06934
--- /dev/null
+++ b/idea/testData/intentions/specifyTypeExplicitly/outClass3.kt
@@ -0,0 +1,8 @@
+open class F
+class B<T>
+class K<out T>
+
+private fun check()<caret> = {
+    class Local : F()
+    B<K<Local>>()
+}
\ No newline at end of file
diff --git a/idea/testData/intentions/specifyTypeExplicitly/outClass3.kt.after b/idea/testData/intentions/specifyTypeExplicitly/outClass3.kt.after
new file mode 100644
index 00000000000..c890ec14fd8
--- /dev/null
+++ b/idea/testData/intentions/specifyTypeExplicitly/outClass3.kt.after
@@ -0,0 +1,8 @@
+open class F
+class B<T>
+class K<out T>
+
+private fun check(): () -> B<*> = {
+    class Local : F()
+    B<K<Local>>()
+}
\ No newline at end of file
diff --git a/idea/tests/org/jetbrains/kotlin/idea/intentions/IntentionTestGenerated.java b/idea/tests/org/jetbrains/kotlin/idea/intentions/IntentionTestGenerated.java
index 060a7c3a689..d6ef10acca6 100644
--- a/idea/tests/org/jetbrains/kotlin/idea/intentions/IntentionTestGenerated.java
+++ b/idea/tests/org/jetbrains/kotlin/idea/intentions/IntentionTestGenerated.java
@@ -16296,11 +16296,31 @@ public class IntentionTestGenerated extends AbstractIntentionTest {
             runTest("idea/testData/intentions/specifyTypeExplicitly/genericClass.kt");
         }
 
+        @TestMetadata("genericClassWithTypeParameters.kt")
+        public void testGenericClassWithTypeParameters() throws Exception {
+            runTest("idea/testData/intentions/specifyTypeExplicitly/genericClassWithTypeParameters.kt");
+        }
+
+        @TestMetadata("genericClassWithTypeParameters2.kt")
+        public void testGenericClassWithTypeParameters2() throws Exception {
+            runTest("idea/testData/intentions/specifyTypeExplicitly/genericClassWithTypeParameters2.kt");
+        }
+
         @TestMetadata("genericFunction.kt")
         public void testGenericFunction() throws Exception {
             runTest("idea/testData/intentions/specifyTypeExplicitly/genericFunction.kt");
         }
 
+        @TestMetadata("innerTypeParameter.kt")
+        public void testInnerTypeParameter() throws Exception {
+            runTest("idea/testData/intentions/specifyTypeExplicitly/innerTypeParameter.kt");
+        }
+
+        @TestMetadata("innerTypeParameter2.kt")
+        public void testInnerTypeParameter2() throws Exception {
+            runTest("idea/testData/intentions/specifyTypeExplicitly/innerTypeParameter2.kt");
+        }
+
         @TestMetadata("lambdaParam.kt")
         public void testLambdaParam() throws Exception {
             runTest("idea/testData/intentions/specifyTypeExplicitly/lambdaParam.kt");
@@ -16311,11 +16331,46 @@ public class IntentionTestGenerated extends AbstractIntentionTest {
             runTest("idea/testData/intentions/specifyTypeExplicitly/localClass.kt");
         }
 
+        @TestMetadata("localClassInSecondTypeParameter.kt")
+        public void testLocalClassInSecondTypeParameter() throws Exception {
+            runTest("idea/testData/intentions/specifyTypeExplicitly/localClassInSecondTypeParameter.kt");
+        }
+
+        @TestMetadata("localClassInSecondTypeParameter2.kt")
+        public void testLocalClassInSecondTypeParameter2() throws Exception {
+            runTest("idea/testData/intentions/specifyTypeExplicitly/localClassInSecondTypeParameter2.kt");
+        }
+
+        @TestMetadata("localClassInSecondTypeParameter3.kt")
+        public void testLocalClassInSecondTypeParameter3() throws Exception {
+            runTest("idea/testData/intentions/specifyTypeExplicitly/localClassInSecondTypeParameter3.kt");
+        }
+
+        @TestMetadata("localClassInTypeParameter.kt")
+        public void testLocalClassInTypeParameter() throws Exception {
+            runTest("idea/testData/intentions/specifyTypeExplicitly/localClassInTypeParameter.kt");
+        }
+
         @TestMetadata("loopParameter.kt")
         public void testLoopParameter() throws Exception {
             runTest("idea/testData/intentions/specifyTypeExplicitly/loopParameter.kt");
         }
 
+        @TestMetadata("outClass.kt")
+        public void testOutClass() throws Exception {
+            runTest("idea/testData/intentions/specifyTypeExplicitly/outClass.kt");
+        }
+
+        @TestMetadata("outClass2.kt")
+        public void testOutClass2() throws Exception {
+            runTest("idea/testData/intentions/specifyTypeExplicitly/outClass2.kt");
+        }
+
+        @TestMetadata("outClass3.kt")
+        public void testOutClass3() throws Exception {
+            runTest("idea/testData/intentions/specifyTypeExplicitly/outClass3.kt");
+        }
+
         @TestMetadata("overriddenAsNull.kt")
         public void testOverriddenAsNull() throws Exception {
             runTest("idea/testData/intentions/specifyTypeExplicitly/overriddenAsNull.kt");