diff --git a/idea/testData/copyPaste/conversion/AddKClassImport.expected.kt b/idea/testData/copyPaste/conversion/AddKClassImport.expected.kt
index bd7fbd1fc81..29ad36b1693 100644
--- a/idea/testData/copyPaste/conversion/AddKClassImport.expected.kt
+++ b/idea/testData/copyPaste/conversion/AddKClassImport.expected.kt
@@ -2,4 +2,4 @@ package to
 
 import kotlin.reflect.KClass
 
-internal annotation class Ann(val value: KClass<Any>)
\ No newline at end of file
+internal annotation class Ann(val value: KClass<*>)
\ No newline at end of file
diff --git a/idea/testData/copyPaste/conversion/RawTypeRef.expected.kt b/idea/testData/copyPaste/conversion/RawTypeRef.expected.kt
index 203dd6d19a3..f773bb36b80 100644
--- a/idea/testData/copyPaste/conversion/RawTypeRef.expected.kt
+++ b/idea/testData/copyPaste/conversion/RawTypeRef.expected.kt
@@ -1 +1 @@
-class B : X<Any>
\ No newline at end of file
+class B : X<*>
\ No newline at end of file
diff --git a/j2k/src/org/jetbrains/kotlin/j2k/TypeVisitor.kt b/j2k/src/org/jetbrains/kotlin/j2k/TypeVisitor.kt
index 3097c958710..39f631e3b64 100644
--- a/j2k/src/org/jetbrains/kotlin/j2k/TypeVisitor.kt
+++ b/j2k/src/org/jetbrains/kotlin/j2k/TypeVisitor.kt
@@ -105,10 +105,7 @@ class TypeVisitor(
         if (classType is PsiClassReferenceType) {
             val targetClass = classType.reference.resolve() as? PsiClass
             if (targetClass != null) {
-                return targetClass.typeParameters.map {
-                    val superType = it.superTypes.first() // there must be at least one super type always
-                    typeConverter.convertType(superType, Nullability.Default, mutability, inAnnotationType).assignNoPrototype()
-                }
+                return targetClass.typeParameters.map { StarProjectionType().assignNoPrototype() }
             }
         }
         return listOf()
diff --git a/j2k/testData/fileOrElement/assignmentExpression/nullability-settings.kt b/j2k/testData/fileOrElement/assignmentExpression/nullability-settings.kt
index 756f549bd86..8b1c1eb4517 100644
--- a/j2k/testData/fileOrElement/assignmentExpression/nullability-settings.kt
+++ b/j2k/testData/fileOrElement/assignmentExpression/nullability-settings.kt
@@ -3,8 +3,8 @@
 import java.util.HashSet
 
 internal class Foo {
-    fun foo(o: HashSet<Any?>?) {
-        val o2: HashSet<Any?>? = o
+    fun foo(o: HashSet<*>?) {
+        val o2: HashSet<*>? = o
         var foo: Int = 0
         foo = o2!!.size
     }
diff --git a/j2k/testData/fileOrElement/assignmentExpression/nullability.kt b/j2k/testData/fileOrElement/assignmentExpression/nullability.kt
index 0510c450899..013c2ca9b26 100644
--- a/j2k/testData/fileOrElement/assignmentExpression/nullability.kt
+++ b/j2k/testData/fileOrElement/assignmentExpression/nullability.kt
@@ -1,7 +1,7 @@
 import java.util.HashSet
 
 internal class Foo {
-    fun foo(o: HashSet<Any>) {
+    fun foo(o: HashSet<*>) {
         val o2 = o
         var foo = 0
         foo = o2.size
diff --git a/j2k/testData/fileOrElement/isOperator/rawType.java b/j2k/testData/fileOrElement/isOperator/rawType.java
new file mode 100644
index 00000000000..b1c995f2297
--- /dev/null
+++ b/j2k/testData/fileOrElement/isOperator/rawType.java
@@ -0,0 +1,8 @@
+import java.util.Collection;
+import java.util.List;
+
+class C {
+    boolean bar(Object o, Collection<String> collection) {
+        return o instanceof Collection && collection instanceof List;
+    }
+}
diff --git a/j2k/testData/fileOrElement/isOperator/rawType.kt b/j2k/testData/fileOrElement/isOperator/rawType.kt
new file mode 100644
index 00000000000..a76f7d22bb1
--- /dev/null
+++ b/j2k/testData/fileOrElement/isOperator/rawType.kt
@@ -0,0 +1,5 @@
+internal class C {
+    fun bar(o: Any, collection: Collection<String>): Boolean {
+        return o is Collection<*> && collection is List<*>
+    }
+}
diff --git a/j2k/testData/fileOrElement/rawGenerics/cycle.java b/j2k/testData/fileOrElement/rawGenerics/cycle.java.todo
similarity index 64%
rename from j2k/testData/fileOrElement/rawGenerics/cycle.java
rename to j2k/testData/fileOrElement/rawGenerics/cycle.java.todo
index dec86461f9c..465ae62dd12 100644
--- a/j2k/testData/fileOrElement/rawGenerics/cycle.java
+++ b/j2k/testData/fileOrElement/rawGenerics/cycle.java.todo
@@ -1,3 +1,4 @@
+//TODO: uncomment this test when KT-12133 fixed
 class JavaClass1<T extends JavaClass2> {
 }
 
diff --git a/j2k/testData/fileOrElement/typeParameters/rawTypeCast.kt b/j2k/testData/fileOrElement/typeParameters/rawTypeCast.kt
index 8bacb776d36..3062919bdf9 100644
--- a/j2k/testData/fileOrElement/typeParameters/rawTypeCast.kt
+++ b/j2k/testData/fileOrElement/typeParameters/rawTypeCast.kt
@@ -1,9 +1,9 @@
-// ERROR: Type inference failed. Expected type mismatch: inferred type is HashMap<Any!, Any!> but Map<String, String> was expected
+// ERROR: Type inference failed. Expected type mismatch: inferred type is HashMap<Any?, Any?> but Map<String, String> was expected
 import java.util.*
 
 internal object A {
     fun foo(): Map<String, String> {
         val props = Properties()
-        return HashMap(props as Map<Any, Any>)
+        return HashMap(props as Map<*, *>)
     }
 }
\ No newline at end of file
diff --git a/j2k/tests/org/jetbrains/kotlin/j2k/JavaToKotlinConverterForWebDemoTestGenerated.java b/j2k/tests/org/jetbrains/kotlin/j2k/JavaToKotlinConverterForWebDemoTestGenerated.java
index 2c137769a76..31f2ee9dcb6 100644
--- a/j2k/tests/org/jetbrains/kotlin/j2k/JavaToKotlinConverterForWebDemoTestGenerated.java
+++ b/j2k/tests/org/jetbrains/kotlin/j2k/JavaToKotlinConverterForWebDemoTestGenerated.java
@@ -2698,6 +2698,12 @@ public class JavaToKotlinConverterForWebDemoTestGenerated extends AbstractJavaTo
             doTest(fileName);
         }
 
+        @TestMetadata("rawType.java")
+        public void testRawType() throws Exception {
+            String fileName = KotlinTestUtils.navigationMetadata("j2k/testData/fileOrElement/isOperator/rawType.java");
+            doTest(fileName);
+        }
+
         @TestMetadata("simpleReference.java")
         public void testSimpleReference() throws Exception {
             String fileName = KotlinTestUtils.navigationMetadata("j2k/testData/fileOrElement/isOperator/simpleReference.java");
@@ -4078,12 +4084,6 @@ public class JavaToKotlinConverterForWebDemoTestGenerated extends AbstractJavaTo
             KotlinTestUtils.assertAllTestsPresentByMetadata(this.getClass(), new File("j2k/testData/fileOrElement/rawGenerics"), Pattern.compile("^(.+)\\.java$"), true);
         }
 
-        @TestMetadata("cycle.java")
-        public void testCycle() throws Exception {
-            String fileName = KotlinTestUtils.navigationMetadata("j2k/testData/fileOrElement/rawGenerics/cycle.java");
-            doTest(fileName);
-        }
-
         @TestMetadata("kt-540.java")
         public void testKt_540() throws Exception {
             String fileName = KotlinTestUtils.navigationMetadata("j2k/testData/fileOrElement/rawGenerics/kt-540.java");
diff --git a/j2k/tests/org/jetbrains/kotlin/j2k/JavaToKotlinConverterSingleFileTestGenerated.java b/j2k/tests/org/jetbrains/kotlin/j2k/JavaToKotlinConverterSingleFileTestGenerated.java
index f0028db8905..6de10f5b4b2 100644
--- a/j2k/tests/org/jetbrains/kotlin/j2k/JavaToKotlinConverterSingleFileTestGenerated.java
+++ b/j2k/tests/org/jetbrains/kotlin/j2k/JavaToKotlinConverterSingleFileTestGenerated.java
@@ -2698,6 +2698,12 @@ public class JavaToKotlinConverterSingleFileTestGenerated extends AbstractJavaTo
             doTest(fileName);
         }
 
+        @TestMetadata("rawType.java")
+        public void testRawType() throws Exception {
+            String fileName = KotlinTestUtils.navigationMetadata("j2k/testData/fileOrElement/isOperator/rawType.java");
+            doTest(fileName);
+        }
+
         @TestMetadata("simpleReference.java")
         public void testSimpleReference() throws Exception {
             String fileName = KotlinTestUtils.navigationMetadata("j2k/testData/fileOrElement/isOperator/simpleReference.java");
@@ -4078,12 +4084,6 @@ public class JavaToKotlinConverterSingleFileTestGenerated extends AbstractJavaTo
             KotlinTestUtils.assertAllTestsPresentByMetadata(this.getClass(), new File("j2k/testData/fileOrElement/rawGenerics"), Pattern.compile("^(.+)\\.java$"), true);
         }
 
-        @TestMetadata("cycle.java")
-        public void testCycle() throws Exception {
-            String fileName = KotlinTestUtils.navigationMetadata("j2k/testData/fileOrElement/rawGenerics/cycle.java");
-            doTest(fileName);
-        }
-
         @TestMetadata("kt-540.java")
         public void testKt_540() throws Exception {
             String fileName = KotlinTestUtils.navigationMetadata("j2k/testData/fileOrElement/rawGenerics/kt-540.java");