diff --git a/compiler/tests/org/jetbrains/jet/jvm/compiler/IdeaJdkAnnotationsReflectedTest.java b/compiler/tests/org/jetbrains/jet/jvm/compiler/IdeaJdkAnnotationsReflectedTest.java
index 6610b8d54d8..59b87d71627 100644
--- a/compiler/tests/org/jetbrains/jet/jvm/compiler/IdeaJdkAnnotationsReflectedTest.java
+++ b/compiler/tests/org/jetbrains/jet/jvm/compiler/IdeaJdkAnnotationsReflectedTest.java
@@ -78,6 +78,11 @@ public class IdeaJdkAnnotationsReflectedTest extends KotlinTestWithEnvironment {
         for (FqName classFqName : JdkAnnotationsValidityTest.getAffectedClasses("jar://ideaSDK/lib/jdkAnnotations.jar!/")) {
             if (new FqName("org.jdom").equals(classFqName.parent())) continue; // filter unrelated jdom annotations
             if (new FqName("java.util.concurrent.TransferQueue").equals(classFqName)) continue; // filter JDK7-specific class
+            // the following idea annotation is incorrect
+            // <item name="java.io.StringWriter void write(java.lang.String) 0">
+            // <annotation name="org.jetbrains.annotations.NotNull" />
+            // </item>
+            if (new FqName("java.io.StringWriter").equals(classFqName)) continue;
 
             PsiClass psiClass = javaPsiFacade.findClass(classFqName.asString(), allScope);
             assertNotNull("Class has annotation, but it is not found: " + classFqName, psiClass);
diff --git a/compiler/tests/org/jetbrains/jet/jvm/compiler/JdkAnnotationsValidityTest.java b/compiler/tests/org/jetbrains/jet/jvm/compiler/JdkAnnotationsValidityTest.java
index c60a32f18fc..fa5914ae4b1 100644
--- a/compiler/tests/org/jetbrains/jet/jvm/compiler/JdkAnnotationsValidityTest.java
+++ b/compiler/tests/org/jetbrains/jet/jvm/compiler/JdkAnnotationsValidityTest.java
@@ -53,9 +53,7 @@ import org.jetbrains.jet.renderer.DescriptorRenderer;
 
 import java.io.File;
 import java.io.IOException;
-import java.util.List;
-import java.util.Map;
-import java.util.Set;
+import java.util.*;
 import java.util.regex.Matcher;
 import java.util.regex.Pattern;
 
@@ -65,6 +63,26 @@ public class JdkAnnotationsValidityTest extends UsefulTestCase {
 
     private static final int CLASSES_IN_CHUNK = 500;
 
+    // KT-4359 Alternative signature checking problem: Set<?> is incompatible with Set<Object>
+    //
+    // <item name='javax.management.openmbean.TabularDataSupport java.util.Set&lt;java.lang.Object&gt; keySet()'>
+    //   <annotation name='org.jetbrains.annotations.NotNull'/>
+    // </item>
+    // <item name='java.util.Map java.util.Set&lt;K&gt; keySet()'>
+    //   <annotation name='org.jetbrains.annotations.NotNull'/>
+    //   <annotation name='jet.runtime.typeinfo.KotlinSignature'>
+    //     <val name="value" val="&quot;fun keySet() : Set&lt;K&gt;&quot;"/>
+    //   </annotation>
+    // </item>
+    // <item name='javax.management.openmbean.TabularData java.util.Set&lt;?&gt; keySet()'>
+    //   <annotation name='org.jetbrains.annotations.NotNull'/>
+    // </item>
+    //
+    // KAnnotator produces above annotations and validation of TabularDataSupport results into:
+    // public open fun keySet(): jet.MutableSet<jet.Any> defined in javax.management.openmbean.TabularDataSupport :
+    // [Incompatible types in superclasses: [Any?, Any, Any], Incompatible projection kinds in type arguments of super methods' return types: [out Any?, Any, Any]]
+    private static final Set<String> classesToIgnore = new HashSet<String>(Arrays.asList("javax.management.openmbean.TabularDataSupport"));
+
     private static JetCoreEnvironment createEnvironment(Disposable parentDisposable) {
         CompilerConfiguration configuration = JetTestUtils.compilerConfigurationForTests(
                 ConfigurationKind.JDK_AND_ANNOTATIONS, TestJdkKind.FULL_JDK, JetTestUtils.getAnnotationsJar());
@@ -152,7 +170,10 @@ public class JdkAnnotationsValidityTest extends UsefulTestCase {
                             String text = StreamUtil.readText(file.getInputStream());
                             Matcher matcher = Pattern.compile("<item name=['\"]([\\w\\d\\.]+)[\\s'\"]").matcher(text);
                             while (matcher.find()) {
-                                result.add(new FqName(matcher.group(1)));
+                                String className = matcher.group(1);
+                                if (!classesToIgnore.contains(className)) {
+                                    result.add(new FqName(className));
+                                }
                             }
                         }
                         catch (IOException e) {