diff --git a/python/testData/override/circle_after.py b/python/testData/override/circle_after.py
index dd4c1d343e98..6fd648ed76aa 100644
--- a/python/testData/override/circle_after.py
+++ b/python/testData/override/circle_after.py
@@ -4,7 +4,7 @@ class Spam(Eggs):
 
 class Eggs(Spam):
   def spam_methods(self):
-      super(Eggs, self).spam_methods()
+      super().spam_methods()
 
   def my_methods(self):
     pass
diff --git a/python/testData/override/classmethodNewStyle_after.py b/python/testData/override/classmethodNewStyle_after.py
index c5e048d6cde2..98f09cfcf529 100644
--- a/python/testData/override/classmethodNewStyle_after.py
+++ b/python/testData/override/classmethodNewStyle_after.py
@@ -6,5 +6,5 @@ class A(object):
 class B(A):
     @classmethod
     def m(cls):
-        <selection>super(B, cls).m()</selection>
+        <selection>super().m()</selection>
 
diff --git a/python/testData/override/classmethod_after.py b/python/testData/override/classmethod_after.py
index dd85fe6b083e..ab342c5c78bf 100644
--- a/python/testData/override/classmethod_after.py
+++ b/python/testData/override/classmethod_after.py
@@ -6,4 +6,4 @@ class A:
 class B(A):
     @classmethod
     def foo(cls):
-        <selection>A.foo(cls)</selection>
+        <selection>super().foo()</selection>
diff --git a/python/testData/override/dunderNew_after.py b/python/testData/override/dunderNew_after.py
index 4770bf402495..bc21e756faca 100644
--- a/python/testData/override/dunderNew_after.py
+++ b/python/testData/override/dunderNew_after.py
@@ -5,5 +5,5 @@ class BaseMeta(type):
 
 class MyMeta(BaseMeta):
     def __new__(cls, name, bases, namespace):
-        return super(MyMeta, cls).__new__(cls, name, bases, namespace)
+        return super().__new__(cls, name, bases, namespace)
 
diff --git a/python/testData/override/indent_after.py b/python/testData/override/indent_after.py
index f51ffeff5a0a..5f676441ef79 100644
--- a/python/testData/override/indent_after.py
+++ b/python/testData/override/indent_after.py
@@ -4,4 +4,4 @@ class Dialog:
 class B(Dialog):
 
     def validate(self):
-        <selection>Dialog.validate(self)</selection>
\ No newline at end of file
+        <selection>super().validate()</selection>
\ No newline at end of file
diff --git a/python/testData/override/innerClass.py b/python/testData/override/innerClass.py
index 8c0eaef2e0b9..cf9941b4d416 100644
--- a/python/testData/override/innerClass.py
+++ b/python/testData/override/innerClass.py
@@ -9,4 +9,4 @@ class A:
 
 class B(A):
     def otherMethod(self, foo, bar):
-        print foo, bar
+        print(foo, bar)
diff --git a/python/testData/override/innerClass_after.py b/python/testData/override/innerClass_after.py
index 5c49802d18bb..b7063ef8ec82 100644
--- a/python/testData/override/innerClass_after.py
+++ b/python/testData/override/innerClass_after.py
@@ -5,10 +5,10 @@ class X(object):
 class A:
     class Inner(X):
         def foo(self):
-            <selection>super(A.Inner, self).foo()</selection>
+            <selection>super().foo()</selection>
 
     def doStuff(self, foo=True): pass
 
 class B(A):
     def otherMethod(self, foo, bar):
-        print foo, bar
+        print(foo, bar)
diff --git a/python/testData/override/innerFunctionClass_after.py b/python/testData/override/innerFunctionClass_after.py
index d1230e14ce08..769e9d7120d1 100644
--- a/python/testData/override/innerFunctionClass_after.py
+++ b/python/testData/override/innerFunctionClass_after.py
@@ -6,5 +6,5 @@ class A():
     def service(self):
         class B(X):
             def foo(self):
-                super(B, self).foo()
+                super().foo()
 
diff --git a/python/testData/override/instanceCheck_after.py b/python/testData/override/instanceCheck_after.py
index fbebd1f526c1..dda1fe7029e0 100644
--- a/python/testData/override/instanceCheck_after.py
+++ b/python/testData/override/instanceCheck_after.py
@@ -1,3 +1,6 @@
+from typing import Any
+
+
 class MyType(type):
-    def __instancecheck__(self, instance):
-        <selection>return super(MyType, self).__instancecheck__(instance)</selection>
+    def __instancecheck__(self, __instance: Any) -> bool:
+        <selection>return super().__instancecheck__(__instance)</selection>
diff --git a/python/testData/override/newStyle.py b/python/testData/override/newStyleClassInPython2.py
similarity index 100%
rename from python/testData/override/newStyle.py
rename to python/testData/override/newStyleClassInPython2.py
diff --git a/python/testData/override/newStyle_after.py b/python/testData/override/newStyleClassInPython2_after.py
similarity index 100%
rename from python/testData/override/newStyle_after.py
rename to python/testData/override/newStyleClassInPython2_after.py
diff --git a/python/testData/override/simple.py b/python/testData/override/oldStyleClassInPython2.py
similarity index 100%
rename from python/testData/override/simple.py
rename to python/testData/override/oldStyleClassInPython2.py
diff --git a/python/testData/override/simple_after.py b/python/testData/override/oldStyleClassInPython2_after.py
similarity index 100%
rename from python/testData/override/simple_after.py
rename to python/testData/override/oldStyleClassInPython2_after.py
diff --git a/python/testData/override/property_after.py b/python/testData/override/property_after.py
index dd3029e2c190..d4d6f170bc8c 100644
--- a/python/testData/override/property_after.py
+++ b/python/testData/override/property_after.py
@@ -7,5 +7,5 @@ class C(object):
 class D(C):
     @property
     def foo(self):
-        return super(D, self).foo
+        return super().foo
 
diff --git a/python/testData/override/qualified_after.py b/python/testData/override/qualified_after.py
index c405b979cfb7..f10cdb3257c4 100644
--- a/python/testData/override/qualified_after.py
+++ b/python/testData/override/qualified_after.py
@@ -1,6 +1,8 @@
 import turtle
+from tkinter import Canvas
+
 
 class C(turtle.TurtleScreenBase):
-    def __init__(self, cv):
-        <selection>super(C, self).__init__(cv)</selection>
+    def __init__(self, cv: Canvas) -> None:
+        <selection>super().__init__(cv)</selection>
 
diff --git a/python/testData/override/returnValue_after.py b/python/testData/override/returnValue_after.py
index 2a0dcb2b65cd..2ea50dce2e54 100644
--- a/python/testData/override/returnValue_after.py
+++ b/python/testData/override/returnValue_after.py
@@ -3,7 +3,7 @@ class A:
 
 class B(A):
     def doStuff(self, foo=True):
-        <selection>return A.doStuff(self, foo)</selection>
+        <selection>return super().doStuff(foo)</selection>
 
     def otherMethod(self, foo, bar):
         print foo, bar
diff --git a/python/testData/override/staticMethod_after.py b/python/testData/override/staticMethod_after.py
index 000c0ca534cf..59653d58d718 100644
--- a/python/testData/override/staticMethod_after.py
+++ b/python/testData/override/staticMethod_after.py
@@ -6,4 +6,4 @@ class A:
 class B(A):
     @staticmethod
     def foo(cls):
-        <selection>A.foo(cls)</selection>
+        <selection>super().foo(cls)</selection>
diff --git a/python/testSrc/com/jetbrains/python/PyOverrideTest.java b/python/testSrc/com/jetbrains/python/PyOverrideTest.java
index d164311fc09d..40b955222b64 100644
--- a/python/testSrc/com/jetbrains/python/PyOverrideTest.java
+++ b/python/testSrc/com/jetbrains/python/PyOverrideTest.java
@@ -1,7 +1,6 @@
 // Copyright 2000-2021 JetBrains s.r.o. Use of this source code is governed by the Apache 2.0 license that can be found in the LICENSE file.
 package com.jetbrains.python;
 
-import com.intellij.testFramework.LightProjectDescriptor;
 import com.intellij.util.ObjectUtils;
 import com.intellij.util.containers.ContainerUtil;
 import com.jetbrains.python.codeInsight.override.PyMethodMember;
@@ -23,11 +22,6 @@ import java.util.List;
 
 public class PyOverrideTest extends PyTestCase {
 
-  @Override
-  protected @Nullable LightProjectDescriptor getProjectDescriptor() {
-    return ourPy2Descriptor;
-  }
-
   private void doTest() {
     doTest(null);
   }
@@ -64,10 +58,6 @@ public class PyOverrideTest extends PyTestCase {
     PyOverrideImplementUtil.overrideMethods(myFixture.getEditor(), subClass, ContainerUtil.map(implToOverride, PyMethodMember::new), false);
   }
 
-  private void doTest3k() {
-    runWithLanguageLevel(LanguageLevel.PYTHON34, this::doTest);
-  }
-
   /**
    * Ensures loops in class hierarchy does not lead to SO
    */
@@ -75,8 +65,8 @@ public class PyOverrideTest extends PyTestCase {
     doTest();
   }
 
-  public void testSimple() {
-    doTest();
+  public void testOldStyleClassInPython2() {
+    runWithLanguageLevel(LanguageLevel.PYTHON27, this::doTest);
   }
 
   public void testClassmethod() {
@@ -87,8 +77,8 @@ public class PyOverrideTest extends PyTestCase {
     doTest();
   }
 
-  public void testNewStyle() {
-    doTest();
+  public void testNewStyleClassInPython2() {
+    runWithLanguageLevel(LanguageLevel.PYTHON27, this::doTest);
   }
 
   public void testReturnValue() {  // PY-1537
@@ -140,17 +130,17 @@ public class PyOverrideTest extends PyTestCase {
   }
 
   public void testPy3k() {
-    doTest3k();
+    doTest();
   }
 
   // PY-15629
   public void testStaticMethodPy3k() {
-    doTest3k();
+    doTest();
   }
 
   // PY-15629
   public void testDunderNewPy3k() {
-    doTest3k();
+    doTest();
   }
 
   // PY-15629
@@ -159,11 +149,11 @@ public class PyOverrideTest extends PyTestCase {
   }
 
   public void testTypeAnnotations() {  // PY-2547
-    doTest3k();
+    doTest();
   }
 
   public void testReturnAnnotation() {  // PY-2690
-    doTest3k();
+    doTest();
   }
 
   // PY-18553
@@ -180,23 +170,21 @@ public class PyOverrideTest extends PyTestCase {
   }
 
   private void doTestImportsForTypeAnnotations() {
-    runWithLanguageLevel(LanguageLevel.PYTHON35, () -> {
-      myFixture.configureByFiles(getTestName(true) + ".py", getTestName(true) + "_import.py");
-      doOverride(null);
-      myFixture.checkResultByFile(getTestName(true) + "_after.py", true);
-    });
+    myFixture.configureByFiles(getTestName(true) + ".py", getTestName(true) + "_import.py");
+    doOverride(null);
+    myFixture.checkResultByFile(getTestName(true) + "_after.py", true);
   }
 
   public void testSingleStar() {  // PY-6455
-    doTest3k();
+    doTest();
   }
 
   public void testStarArgs() {  // PY-6455
-    doTest3k();
+    doTest();
   }
 
   public void testKwargs() {  // PY-7401
-    doTest3k();
+    doTest();
   }
 
   public void testDocstring() {
@@ -210,26 +198,24 @@ public class PyOverrideTest extends PyTestCase {
 
   // PY-19312
   public void testAsyncMethod() {
-    runWithLanguageLevel(LanguageLevel.PYTHON36, this::doTest);
+    doTest();
   }
 
   // PY-30287
   public void testMethodWithOverloadsInTheSameFile() {
-    runWithLanguageLevel(LanguageLevel.PYTHON35, this::doTest);
+    doTest();
   }
 
   // PY-30287
   public void testMethodWithOverloadsInAnotherFile() {
-    runWithLanguageLevel(LanguageLevel.PYTHON35, () -> {
-      myFixture.configureByFiles(getTestName(true) + ".py", getTestName(true) + "_parent.py");
-      doOverride(null);
-      myFixture.checkResultByFile(getTestName(true) + "_after.py", true);
-    });
+    myFixture.configureByFiles(getTestName(true) + ".py", getTestName(true) + "_parent.py");
+    doOverride("B");
+    myFixture.checkResultByFile(getTestName(true) + "_after.py", true);
   }
 
   // PY-35512
   public void testPositionalOnlyParameters() {
-    runWithLanguageLevel(LanguageLevel.PYTHON38, () -> doTest("B"));
+    doTest("B");
   }
 
   @Override