diff --git a/Lib/test/test_shutil.py b/Lib/test/test_shutil.py
index 4cc18039ad678c..b3d5a26e48ca80 100644
--- a/Lib/test/test_shutil.py
+++ b/Lib/test/test_shutil.py
@@ -638,108 +638,62 @@ def test_rmtree_on_junction(self):
         finally:
             shutil.rmtree(TESTFN, ignore_errors=True)
 
-    def test_rmtree_deleted_file_race_condition(self):
-        # bpo-37260
-        #
-        # Test that a file deleted after it is enumerated
-        # by scandir() but before unlink() is called
-        # doesn't generate any errors.
-        def _onexc(fn, path, exc):
-            if path == paths[0]:
-                os.chmod(paths[0], mode)
-                os.rmdir(paths[0])
-                os.unlink(paths[1])
-                pass
-            else:
-                raise
-
-        paths = [os.path.join(TESTFN, 'foo'),
-                 os.path.join(TESTFN, 'bar')]
-        os.mkdir(TESTFN)
-        os.mkdir(paths[0])
-        write_file((TESTFN, 'bar'), 'bar')
-        mode = os.stat(paths[0]).st_mode
-        os.chmod(paths[0], 0)
-
-        try:
-            shutil.rmtree(TESTFN, onexc=_onexc)
-        except:
-            # test failed, so cleanup artifacts
-            try:
-                os.chmod(paths[0], mode)
-            except:
-                pass
-
-            shutil.rmtree(TESTFN)
-
-    def test_rmtree_deleted_dir_race_condition(self):
-        # bpo-37260
-        #
-        # Test that a directory deleted after it is enumerated
-        # by scandir() but before rmdr() is called
-        # doesn't generate any errors.
-        def _onexc(fn, path, exc):
-            if path == paths[0]:
-                os.chmod(paths[0], mode)
-                os.rmdir(paths[0])
-                os.rmdir(paths[1])
-                pass
-            else:
-                raise
-
-        paths = [os.path.join(TESTFN, 'foo'),
-                 os.path.join(TESTFN, 'bar')]
-        os.mkdir(TESTFN)
-        os.mkdir(paths[0])
-        os.mkdir(paths[1])
-        mode = os.stat(paths[0]).st_mode
-        os.chmod(paths[0], 0)
-
-        try:
-            shutil.rmtree(TESTFN, onexc=_onexc)
-        except:
-            # test failed, so cleanup artifacts
-            try:
-                os.chmod(paths[0], mode)
-            except:
-                pass
-
-            shutil.rmtree(TESTFN)
-
-    @os_helper.skip_unless_symlink
-    def test_rmtree_deleted_symlink_race_condition(self):
+    @unittest.skipIf(sys.platform[:6] == 'cygwin',
+                     "This test can't be run on Cygwin (issue #1071513).")
+    @os_helper.skip_if_dac_override
+    @os_helper.skip_unless_working_chmod
+    def test_rmtree_deleted_race_condition(self):
         # bpo-37260
         #
-        # Test that a symlink deleted after it is enumerated
-        # by scandir() but before unlink() is called
-        # doesn't generate any errors.
+        # Test that a file or a directory deleted after it is enumerated
+        # by scandir() but before unlink() or rmdr() is called doesn't
+        # generate any errors.
         def _onexc(fn, path, exc):
-            if path == paths[0]:
-                os.chmod(paths[0], mode)
-                os.rmdir(paths[0])
-                os.unlink(paths[1])
-                pass
-            else:
+            assert fn in (os.rmdir, os.unlink)
+            if not isinstance(exc, PermissionError):
                 raise
+            # Make the parent and the children writeable.
+            for p, mode in zip(paths, old_modes):
+                os.chmod(p, mode)
+            # Remove other dirs except one.
+            keep = next(p for p in dirs if p != path)
+            for p in dirs:
+                if p != keep:
+                    os.rmdir(p)
+            # Remove other files except one.
+            keep = next(p for p in files if p != path)
+            for p in files:
+                if p != keep:
+                    os.unlink(p)
 
-        paths = [os.path.join(TESTFN, 'foo'),
-                 os.path.join(TESTFN, 'bar')]
         os.mkdir(TESTFN)
-        os.mkdir(paths[0])
-        os.symlink('foo', paths[1])
-        mode = os.stat(paths[0]).st_mode
-        os.chmod(paths[0], 0)
+        paths = [TESTFN] + [os.path.join(TESTFN, f'child{i}')
+                            for i in range(6)]
+        dirs = paths[1::2]
+        files = paths[2::2]
+        for path in dirs:
+            os.mkdir(path)
+        for path in files:
+            write_file(path, '')
+
+        old_modes = [os.stat(path).st_mode for path in paths]
+
+        # Make the parent and the children non-writeable.
+        new_mode = stat.S_IREAD|stat.S_IEXEC
+        for path in reversed(paths):
+            os.chmod(path, new_mode)
 
         try:
             shutil.rmtree(TESTFN, onexc=_onexc)
         except:
-            # test failed, so cleanup artifacts
-            try:
-                os.chmod(paths[0], mode)
-            except:
-                pass
-
+            # Test failed, so cleanup artifacts.
+            for path, mode in zip(paths, old_modes):
+                try:
+                    os.chmod(path, mode)
+                except OSError:
+                    pass
             shutil.rmtree(TESTFN)
+            raise
 
 
 class TestCopyTree(BaseTest, unittest.TestCase):