diff --git a/idea/ide-common/src/org/jetbrains/kotlin/idea/util/FuzzyType.kt b/idea/ide-common/src/org/jetbrains/kotlin/idea/util/FuzzyType.kt
index b1535681860..c50f15946bb 100644
--- a/idea/ide-common/src/org/jetbrains/kotlin/idea/util/FuzzyType.kt
+++ b/idea/ide-common/src/org/jetbrains/kotlin/idea/util/FuzzyType.kt
@@ -16,7 +16,6 @@
 
 package org.jetbrains.kotlin.idea.util
 
-import org.jetbrains.kotlin.builtins.KotlinBuiltIns
 import org.jetbrains.kotlin.descriptors.CallableDescriptor
 import org.jetbrains.kotlin.descriptors.TypeParameterDescriptor
 import org.jetbrains.kotlin.resolve.calls.inference.ConstraintSystemImpl
@@ -42,7 +41,7 @@ fun FuzzyType.makeNotNullable() = FuzzyType(type.makeNotNullable(), freeParamete
 fun FuzzyType.makeNullable() = FuzzyType(type.makeNullable(), freeParameters)
 fun FuzzyType.nullability() = type.nullability()
 
-fun FuzzyType.isAlmostAnyType(): Boolean {
+fun FuzzyType.isAlmostEverything(): Boolean {
     if (freeParameters.isEmpty()) return false
     val typeParameter = type.constructor.declarationDescriptor as? TypeParameterDescriptor ?: return false
     if (typeParameter !in freeParameters) return false
diff --git a/idea/idea-completion/src/org/jetbrains/kotlin/idea/completion/ExpectedInfos.kt b/idea/idea-completion/src/org/jetbrains/kotlin/idea/completion/ExpectedInfos.kt
index a3ade125b0a..40f8c0f223b 100644
--- a/idea/idea-completion/src/org/jetbrains/kotlin/idea/completion/ExpectedInfos.kt
+++ b/idea/idea-completion/src/org/jetbrains/kotlin/idea/completion/ExpectedInfos.kt
@@ -25,7 +25,6 @@ import org.jetbrains.kotlin.idea.completion.smart.toList
 import org.jetbrains.kotlin.idea.core.mapArgumentsToParameters
 import org.jetbrains.kotlin.idea.util.FuzzyType
 import org.jetbrains.kotlin.idea.util.fuzzyReturnType
-import org.jetbrains.kotlin.idea.util.isAlmostAnyType
 import org.jetbrains.kotlin.lexer.JetTokens
 import org.jetbrains.kotlin.name.Name
 import org.jetbrains.kotlin.psi.*
@@ -51,7 +50,7 @@ import org.jetbrains.kotlin.types.TypeUtils
 import org.jetbrains.kotlin.types.expressions.ExpressionTypingUtils
 import org.jetbrains.kotlin.types.typeUtil.containsError
 import org.jetbrains.kotlin.types.typeUtil.makeNotNullable
-import java.util.*
+import java.util.LinkedHashSet
 
 enum class Tail {
     COMMA,
@@ -146,7 +145,11 @@ class ExpectedInfos(
                     ?.map { it.fuzzyType } ?: return results
             if (expectedFuzzyTypes.isEmpty() || expectedFuzzyTypes.any { it.freeParameters.isNotEmpty() }) return results
 
-            return expectedFuzzyTypes.flatMap { calculateForArgument(call, it.type, argument) ?: emptyList() }.toSet()
+            return expectedFuzzyTypes
+                    .map { it.type }
+                    .toSet()
+                    .flatMap { calculateForArgument(call, it, argument) ?: emptyList() }
+                    .toSet()
         }
 
         return results
@@ -200,6 +203,7 @@ class ExpectedInfos(
             var argumentToParameter = call.mapArgumentsToParameters(descriptor)
             var parameter = argumentToParameter[argument] ?: continue
 
+            //TODO: we can loose partially inferred substitution here but what to do?
             if (parameter.type.containsError()) {
                 parameter = parameter.original
                 descriptor = descriptor.original
diff --git a/idea/idea-completion/src/org/jetbrains/kotlin/idea/completion/SmartCompletionSession.kt b/idea/idea-completion/src/org/jetbrains/kotlin/idea/completion/SmartCompletionSession.kt
index 3fa39e03845..5db1a35e1ed 100644
--- a/idea/idea-completion/src/org/jetbrains/kotlin/idea/completion/SmartCompletionSession.kt
+++ b/idea/idea-completion/src/org/jetbrains/kotlin/idea/completion/SmartCompletionSession.kt
@@ -107,7 +107,7 @@ class SmartCompletionSession(configuration: CompletionSessionConfiguration, para
                         override fun getValueArgumentList() = throw UnsupportedOperationException()
                     }
 
-                    val expectedInfos = ExpectedInfos(bindingContext, resolutionFacade, moduleDescriptor, useHeuristicSignatures = false)
+                    val expectedInfos = ExpectedInfos(bindingContext, resolutionFacade, moduleDescriptor)
                             .calculateForArgument(dummyCall, dummyArgument)
                     if (expectedInfos != null) {
                         collector.addElements(LambdaItems.collect(expectedInfos))
diff --git a/idea/idea-completion/src/org/jetbrains/kotlin/idea/completion/smart/SmartCompletion.kt b/idea/idea-completion/src/org/jetbrains/kotlin/idea/completion/smart/SmartCompletion.kt
index 082876c6ed4..265ed4e21ad 100644
--- a/idea/idea-completion/src/org/jetbrains/kotlin/idea/completion/smart/SmartCompletion.kt
+++ b/idea/idea-completion/src/org/jetbrains/kotlin/idea/completion/smart/SmartCompletion.kt
@@ -39,7 +39,9 @@ import org.jetbrains.kotlin.resolve.BindingContext
 import org.jetbrains.kotlin.resolve.DescriptorUtils
 import org.jetbrains.kotlin.types.JetType
 import org.jetbrains.kotlin.types.TypeUtils
-import org.jetbrains.kotlin.types.typeUtil.*
+import org.jetbrains.kotlin.types.typeUtil.TypeNullability
+import org.jetbrains.kotlin.types.typeUtil.isNothing
+import org.jetbrains.kotlin.types.typeUtil.makeNotNullable
 import java.util.ArrayList
 import java.util.HashSet
 
@@ -210,7 +212,7 @@ class SmartCompletion(
             var returnType = fuzzyReturnType() ?: return listOf()
             // skip declarations of type Nothing or of generic parameter type which has no real bounds
             //TODO: maybe we should include them on the second press?
-            if (returnType.type.isNothing() || returnType.isAlmostAnyType()) return listOf()
+            if (returnType.type.isNothing() || returnType.isAlmostEverything()) return listOf()
 
             if (this is VariableDescriptor) {
                 return smartCastTypes(this).map { FuzzyType(it, listOf()) }
@@ -244,7 +246,7 @@ class SmartCompletion(
         while (true) {
             val infos = ExpectedInfos(bindingContext, resolutionFacade, moduleDescriptor, useOuterCallsExpectedTypeCount = count)
                     .calculate(expression) ?: return null
-            if (count == 2 /* use two outer calls maximum */ || infos.none { it.fuzzyType.isAlmostAnyType() }) return infos
+            if (count == 2 /* use two outer calls maximum */ || infos.none { it.fuzzyType.isAlmostEverything() }) return infos
             count++
         }
         //TODO: we could always give higher priority to results with outer call expected type used
diff --git a/idea/idea-completion/testData/smart/FilterTo.kt b/idea/idea-completion/testData/smart/FilterTo.kt
new file mode 100644
index 00000000000..033a4c0fab7
--- /dev/null
+++ b/idea/idea-completion/testData/smart/FilterTo.kt
@@ -0,0 +1,8 @@
+fun foo(list: List<String>, intList: MutableList<Int>, stringList: MutableList<String>, p: Any) {
+    list.filterTo(<caret>)
+}
+
+// EXIST: arrayListOf
+// EXIST: stringList
+// ABSENT: intList
+// ABSENT: p
diff --git a/idea/idea-completion/testData/smart/LambdaValue3.kt b/idea/idea-completion/testData/smart/LambdaValue3.kt
index 29ff33895d6..a60f4368b6a 100644
--- a/idea/idea-completion/testData/smart/LambdaValue3.kt
+++ b/idea/idea-completion/testData/smart/LambdaValue3.kt
@@ -1,4 +1,4 @@
-fun foo(list: List<String>): Collection<Int> {
+fun foo(list: List<String>) {
     bar(list.map { it.<caret> })
 }
 
diff --git a/idea/idea-completion/testData/smart/MapTo.kt b/idea/idea-completion/testData/smart/MapTo.kt
index 59877a17126..5bc9c0aff96 100644
--- a/idea/idea-completion/testData/smart/MapTo.kt
+++ b/idea/idea-completion/testData/smart/MapTo.kt
@@ -1,7 +1,8 @@
-fun foo(list: List<String>, intList: MutableList<Int>, stringList: MutableList<String>): Collection<Int> {
+fun foo(list: List<String>, intList: MutableList<Int>, stringList: MutableList<String>, p: Any): Collection<Int> {
     return list.mapTo(<caret>)
 }
 
 // EXIST: intList
 // EXIST: arrayListOf
 // EXIST: stringList
+// ABSENT: p
diff --git a/idea/idea-completion/testData/smart/MapTo2.kt b/idea/idea-completion/testData/smart/MapTo2.kt
index de9ce76e637..90e4cdb1de2 100644
--- a/idea/idea-completion/testData/smart/MapTo2.kt
+++ b/idea/idea-completion/testData/smart/MapTo2.kt
@@ -1,7 +1,8 @@
-fun foo(list: List<String>, intList: MutableList<Int>, stringList: MutableList<String>): Collection<Int> {
+fun foo(list: List<String>, intList: MutableList<Int>, stringList: MutableList<String>, p: Any): Collection<Int> {
     list.mapTo(<caret>)
 }
 
 // EXIST: intList
 // EXIST: stringList
 // EXIST: arrayListOf
+// ABSENT: p
diff --git a/idea/idea-completion/tests/org/jetbrains/kotlin/idea/completion/test/JvmSmartCompletionTestGenerated.java b/idea/idea-completion/tests/org/jetbrains/kotlin/idea/completion/test/JvmSmartCompletionTestGenerated.java
index 36495467d43..782868410a4 100644
--- a/idea/idea-completion/tests/org/jetbrains/kotlin/idea/completion/test/JvmSmartCompletionTestGenerated.java
+++ b/idea/idea-completion/tests/org/jetbrains/kotlin/idea/completion/test/JvmSmartCompletionTestGenerated.java
@@ -131,6 +131,12 @@ public class JvmSmartCompletionTestGenerated extends AbstractJvmSmartCompletionT
         doTest(fileName);
     }
 
+    @TestMetadata("FilterTo.kt")
+    public void testFilterTo() throws Exception {
+        String fileName = JetTestUtils.navigationMetadata("idea/idea-completion/testData/smart/FilterTo.kt");
+        doTest(fileName);
+    }
+
     @TestMetadata("GroupBySubstitutor.kt")
     public void testGroupBySubstitutor() throws Exception {
         String fileName = JetTestUtils.navigationMetadata("idea/idea-completion/testData/smart/GroupBySubstitutor.kt");