diff --git a/idea/src/org/jetbrains/kotlin/idea/intentions/SpecifyTypeExplicitlyIntention.kt b/idea/src/org/jetbrains/kotlin/idea/intentions/SpecifyTypeExplicitlyIntention.kt
index 306970b4b59..c715237fc08 100644
--- a/idea/src/org/jetbrains/kotlin/idea/intentions/SpecifyTypeExplicitlyIntention.kt
+++ b/idea/src/org/jetbrains/kotlin/idea/intentions/SpecifyTypeExplicitlyIntention.kt
@@ -23,16 +23,15 @@ import com.intellij.psi.PsiDocumentManager
 import org.jetbrains.kotlin.builtins.KotlinBuiltIns
 import org.jetbrains.kotlin.descriptors.CallableDescriptor
 import org.jetbrains.kotlin.idea.caches.resolve.analyze
-import org.jetbrains.kotlin.idea.util.IdeDescriptorRenderers
-import org.jetbrains.kotlin.idea.util.ShortenReferences
+import org.jetbrains.kotlin.idea.caches.resolve.getResolutionFacade
+import org.jetbrains.kotlin.idea.util.*
 import org.jetbrains.kotlin.psi.*
 import org.jetbrains.kotlin.psi.psiUtil.getElementTextWithContext
 import org.jetbrains.kotlin.resolve.BindingContext
-import org.jetbrains.kotlin.resolve.DescriptorUtils
-import org.jetbrains.kotlin.types.ErrorUtils
-import org.jetbrains.kotlin.types.KotlinType
-import org.jetbrains.kotlin.types.TypeUtils
-import java.util.*
+import org.jetbrains.kotlin.resolve.lazy.BodyResolveMode
+import org.jetbrains.kotlin.types.*
+import org.jetbrains.kotlin.utils.SmartSet
+import org.jetbrains.kotlin.utils.addToStdlib.singletonList
 
 public class SpecifyTypeExplicitlyIntention : SelfTargetingIntention<KtCallableDeclaration>(KtCallableDeclaration::class.java, "Specify type explicitly"), LowPriorityAction {
     override fun isApplicableTo(element: KtCallableDeclaration, caretOffset: Int): Boolean {
@@ -65,14 +64,34 @@ public class SpecifyTypeExplicitlyIntention : SelfTargetingIntention<KtCallableD
             return type ?: ErrorUtils.createErrorType("null type")
         }
 
-        public fun createTypeExpressionForTemplate(exprType: KotlinType): Expression {
-            val descriptor = exprType.constructor.declarationDescriptor
-            val isAnonymous = descriptor != null && DescriptorUtils.isAnonymousObject(descriptor)
+        public fun createTypeExpressionForTemplate(exprType: KotlinType, contextElement: KtElement): Expression {
+            val resolutionFacade = contextElement.getResolutionFacade()
+            val bindingContext = resolutionFacade.analyze(contextElement, BodyResolveMode.PARTIAL)
+            val scope = contextElement.getResolutionScope(bindingContext, resolutionFacade)
+            val types = (exprType.singletonList() + TypeUtils.getAllSupertypes(exprType))
+                    .filter { it.isResolvableInScope(scope, true) }
+                    .mapNotNull mapArgs@ {
+                        val resolvableArgs = it.arguments.filterTo(SmartSet.create()) { it.type.isResolvableInScope(scope, true) }
+                        if (resolvableArgs.containsAll(it.arguments)) return@mapArgs it
 
-            val allSupertypes = TypeUtils.getAllSupertypes(exprType)
-            val types = if (isAnonymous) ArrayList<KotlinType>() else arrayListOf(exprType)
-            types.addAll(allSupertypes)
+                        val newArguments = (it.arguments zip it.constructor.parameters).map {
+                            val (arg, param) = it
+                            when {
+                                arg in resolvableArgs -> arg
+                                arg.projectionKind == Variance.OUT_VARIANCE ||
+                                param.variance == Variance.OUT_VARIANCE -> TypeProjectionImpl(
+                                        arg.projectionKind,
+                                        arg.type.approximateWithResolvableType(scope, true)
+                                )
+                                else -> return@mapArgs null
+                            }
+                        }
 
+                        object: DelegatingType() {
+                            override fun getDelegate() = it
+                            override fun getArguments() = newArguments
+                        }
+                    }
             return object : ChooseValueExpression<KotlinType>(types, types.first()) {
                 override fun getLookupString(element: KotlinType) = IdeDescriptorRenderers.SOURCE_CODE_SHORT_NAMES_IN_TYPES.renderType(element)
                 override fun getResult(element: KotlinType) = IdeDescriptorRenderers.SOURCE_CODE.renderType(element)
@@ -103,7 +122,7 @@ public class SpecifyTypeExplicitlyIntention : SelfTargetingIntention<KtCallableD
             assert(!exprType.isError) { "Unexpected error type, should have been checked before: " + declaration.getElementTextWithContext() + ", type = " + exprType }
 
             val project = declaration.project
-            val expression = createTypeExpressionForTemplate(exprType)
+            val expression = createTypeExpressionForTemplate(exprType, declaration)
 
             declaration.setType(KotlinBuiltIns.FQ_NAMES.any.asString())
 
diff --git a/idea/src/org/jetbrains/kotlin/idea/refactoring/introduce/introduceVariable/KotlinInplaceVariableIntroducer.java b/idea/src/org/jetbrains/kotlin/idea/refactoring/introduce/introduceVariable/KotlinInplaceVariableIntroducer.java
index 3cb0bcf1e3a..92276963872 100644
--- a/idea/src/org/jetbrains/kotlin/idea/refactoring/introduce/introduceVariable/KotlinInplaceVariableIntroducer.java
+++ b/idea/src/org/jetbrains/kotlin/idea/refactoring/introduce/introduceVariable/KotlinInplaceVariableIntroducer.java
@@ -356,7 +356,7 @@ public class KotlinInplaceVariableIntroducer<D extends KtCallableDeclaration> ex
         if (typeReference != null) {
             builder.replaceElement(typeReference,
                                    TYPE_REFERENCE_VARIABLE_NAME,
-                                   SpecifyTypeExplicitlyIntention.Companion.createTypeExpressionForTemplate(myExprType),
+                                   SpecifyTypeExplicitlyIntention.Companion.createTypeExpressionForTemplate(myExprType, myDeclaration),
                                    false);
         }
     }
diff --git a/idea/src/org/jetbrains/kotlin/idea/refactoring/introduce/introduceVariable/KotlinVariableInplaceIntroducer.kt b/idea/src/org/jetbrains/kotlin/idea/refactoring/introduce/introduceVariable/KotlinVariableInplaceIntroducer.kt
index a109cb851a2..52a915122c1 100644
--- a/idea/src/org/jetbrains/kotlin/idea/refactoring/introduce/introduceVariable/KotlinVariableInplaceIntroducer.kt
+++ b/idea/src/org/jetbrains/kotlin/idea/refactoring/introduce/introduceVariable/KotlinVariableInplaceIntroducer.kt
@@ -109,7 +109,7 @@ public class KotlinVariableInplaceIntroducer(
         addedVariable.typeReference?.let {
             builder.replaceElement(it,
                                    "TypeReferenceVariable",
-                                   SpecifyTypeExplicitlyIntention.createTypeExpressionForTemplate(expressionType!!),
+                                   SpecifyTypeExplicitlyIntention.createTypeExpressionForTemplate(expressionType!!, addedVariable),
                                    false)
         }
     }
diff --git a/idea/testData/intentions/specifyTypeExplicitly/anonymousObject.kt b/idea/testData/intentions/specifyTypeExplicitly/anonymousObject.kt
new file mode 100644
index 00000000000..a033868e63b
--- /dev/null
+++ b/idea/testData/intentions/specifyTypeExplicitly/anonymousObject.kt
@@ -0,0 +1,3 @@
+class A {
+    private fun foo() <caret>= { object {} }
+}
\ No newline at end of file
diff --git a/idea/testData/intentions/specifyTypeExplicitly/anonymousObject.kt.after b/idea/testData/intentions/specifyTypeExplicitly/anonymousObject.kt.after
new file mode 100644
index 00000000000..374168dfb5a
--- /dev/null
+++ b/idea/testData/intentions/specifyTypeExplicitly/anonymousObject.kt.after
@@ -0,0 +1,3 @@
+class A {
+    private fun foo(): () -> Any<caret> = { object {} }
+}
\ No newline at end of file
diff --git a/idea/testData/intentions/specifyTypeExplicitly/localClass.kt b/idea/testData/intentions/specifyTypeExplicitly/localClass.kt
new file mode 100644
index 00000000000..a9d9ab11fef
--- /dev/null
+++ b/idea/testData/intentions/specifyTypeExplicitly/localClass.kt
@@ -0,0 +1,6 @@
+class A {
+    private fun bar() <caret>= {
+        class Local()
+        Local()
+    }
+}
\ No newline at end of file
diff --git a/idea/testData/intentions/specifyTypeExplicitly/localClass.kt.after b/idea/testData/intentions/specifyTypeExplicitly/localClass.kt.after
new file mode 100644
index 00000000000..7bde653b217
--- /dev/null
+++ b/idea/testData/intentions/specifyTypeExplicitly/localClass.kt.after
@@ -0,0 +1,6 @@
+class A {
+    private fun bar(): () -> Any<caret> = {
+        class Local()
+        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 ab9c40aee82..fbcf5e0f511 100644
--- a/idea/tests/org/jetbrains/kotlin/idea/intentions/IntentionTestGenerated.java
+++ b/idea/tests/org/jetbrains/kotlin/idea/intentions/IntentionTestGenerated.java
@@ -7906,6 +7906,12 @@ public class IntentionTestGenerated extends AbstractIntentionTest {
             KotlinTestUtils.assertAllTestsPresentByMetadata(this.getClass(), new File("idea/testData/intentions/specifyTypeExplicitly"), Pattern.compile("^([\\w\\-_]+)\\.kt$"), true);
         }
 
+        @TestMetadata("anonymousObject.kt")
+        public void testAnonymousObject() throws Exception {
+            String fileName = KotlinTestUtils.navigationMetadata("idea/testData/intentions/specifyTypeExplicitly/anonymousObject.kt");
+            doTest(fileName);
+        }
+
         @TestMetadata("badCaretPosition.kt")
         public void testBadCaretPosition() throws Exception {
             String fileName = KotlinTestUtils.navigationMetadata("idea/testData/intentions/specifyTypeExplicitly/badCaretPosition.kt");
@@ -7942,6 +7948,12 @@ public class IntentionTestGenerated extends AbstractIntentionTest {
             doTest(fileName);
         }
 
+        @TestMetadata("localClass.kt")
+        public void testLocalClass() throws Exception {
+            String fileName = KotlinTestUtils.navigationMetadata("idea/testData/intentions/specifyTypeExplicitly/localClass.kt");
+            doTest(fileName);
+        }
+
         @TestMetadata("loopParameter.kt")
         public void testLoopParameter() throws Exception {
             String fileName = KotlinTestUtils.navigationMetadata("idea/testData/intentions/specifyTypeExplicitly/loopParameter.kt");