diff --git a/django/test/runner.py b/django/test/runner.py
index 46c8c5842d..72863aa8fe 100644
--- a/django/test/runner.py
+++ b/django/test/runner.py
@@ -779,7 +779,7 @@ def reorder_suite(suite, classes, reverse=False):
     bins = [OrderedSet() for i in range(len(classes) + 1)]
     *class_bins, last_bin = bins
 
-    for test in iter_test_cases(suite, reverse=reverse):
+    for test in iter_test_cases(suite):
         for test_bin, test_class in zip(class_bins, classes):
             if isinstance(test, test_class):
                 break
@@ -787,6 +787,8 @@ def reorder_suite(suite, classes, reverse=False):
             test_bin = last_bin
         test_bin.add(test)
 
+    if reverse:
+        bins = (reversed(tests) for tests in bins)
     suite_class = type(suite)
     return suite_class(itertools.chain(*bins))
 
diff --git a/django/test/utils.py b/django/test/utils.py
index 638bcd6fb5..c1bfc87fc0 100644
--- a/django/test/utils.py
+++ b/django/test/utils.py
@@ -235,16 +235,14 @@ def setup_databases(
     return old_names
 
 
-def iter_test_cases(suite, reverse=False):
+def iter_test_cases(suite):
     """Return an iterator over a test suite's unittest.TestCase objects."""
-    if reverse:
-        suite = reversed(tuple(suite))
     for test in suite:
         if isinstance(test, TestCase):
             yield test
         else:
             # Otherwise, assume it is a test suite.
-            yield from iter_test_cases(test, reverse=reverse)
+            yield from iter_test_cases(test)
 
 
 def dependency_ordered(test_databases, dependencies):
diff --git a/tests/test_runner/tests.py b/tests/test_runner/tests.py
index 8a071d0c8d..27a03fdda0 100644
--- a/tests/test_runner/tests.py
+++ b/tests/test_runner/tests.py
@@ -14,7 +14,7 @@ from django.core.management.base import SystemCheckError
 from django.test import (
     SimpleTestCase, TransactionTestCase, skipUnlessDBFeature,
 )
-from django.test.runner import DiscoverRunner
+from django.test.runner import DiscoverRunner, reorder_suite
 from django.test.testcases import connections_support_transactions
 from django.test.utils import (
     captured_stderr, dependency_ordered, get_unique_databases_and_mirrors,
@@ -36,13 +36,25 @@ class MySuite:
         yield from self.tests
 
 
-class IterTestCasesTests(unittest.TestCase):
-    def make_test_suite(self, suite=None, suite_class=None):
+class TestSuiteTests(unittest.TestCase):
+    def build_test_suite(self, test_classes, suite=None, suite_class=None):
         if suite_class is None:
             suite_class = unittest.TestSuite
         if suite is None:
             suite = suite_class()
 
+        loader = unittest.defaultTestLoader
+        for test_class in test_classes:
+            tests = loader.loadTestsFromTestCase(test_class)
+            subsuite = suite_class()
+            # Only use addTest() to simplify testing a custom TestSuite.
+            for test in tests:
+                subsuite.addTest(test)
+            suite.addTest(subsuite)
+
+        return suite
+
+    def make_test_suite(self, suite=None, suite_class=None):
         class Tests1(unittest.TestCase):
             def test1(self):
                 pass
@@ -57,16 +69,11 @@ class IterTestCasesTests(unittest.TestCase):
             def test2(self):
                 pass
 
-        loader = unittest.defaultTestLoader
-        for test_cls in (Tests1, Tests2):
-            tests = loader.loadTestsFromTestCase(test_cls)
-            subsuite = suite_class()
-            # Only use addTest() to simplify testing a custom TestSuite.
-            for test in tests:
-                subsuite.addTest(test)
-            suite.addTest(subsuite)
-
-        return suite
+        return self.build_test_suite(
+            (Tests1, Tests2),
+            suite=suite,
+            suite_class=suite_class,
+        )
 
     def assertTestNames(self, tests, expected):
         # Each test.id() has a form like the following:
@@ -75,28 +82,21 @@ class IterTestCasesTests(unittest.TestCase):
         names = ['.'.join(test.id().split('.')[-2:]) for test in tests]
         self.assertEqual(names, expected)
 
-    def test_basic(self):
+    def test_iter_test_cases_basic(self):
         suite = self.make_test_suite()
         tests = iter_test_cases(suite)
         self.assertTestNames(tests, expected=[
             'Tests1.test1', 'Tests1.test2', 'Tests2.test1', 'Tests2.test2',
         ])
 
-    def test_reverse(self):
-        suite = self.make_test_suite()
-        tests = iter_test_cases(suite, reverse=True)
-        self.assertTestNames(tests, expected=[
-            'Tests2.test2', 'Tests2.test1', 'Tests1.test2', 'Tests1.test1',
-        ])
-
-    def test_custom_test_suite_class(self):
+    def test_iter_test_cases_custom_test_suite_class(self):
         suite = self.make_test_suite(suite_class=MySuite)
         tests = iter_test_cases(suite)
         self.assertTestNames(tests, expected=[
             'Tests1.test1', 'Tests1.test2', 'Tests2.test1', 'Tests2.test2',
         ])
 
-    def test_mixed_test_suite_classes(self):
+    def test_iter_test_cases_mixed_test_suite_classes(self):
         suite = self.make_test_suite(suite=MySuite())
         child_suite = list(suite)[0]
         self.assertNotIsInstance(child_suite, MySuite)
@@ -104,6 +104,33 @@ class IterTestCasesTests(unittest.TestCase):
         self.assertEqual(len(tests), 4)
         self.assertNotIsInstance(tests[0], unittest.TestSuite)
 
+    def test_reorder_suite_reverse_with_duplicates(self):
+        class Tests1(unittest.TestCase):
+            def test1(self):
+                pass
+
+        class Tests2(unittest.TestCase):
+            def test2(self):
+                pass
+
+            def test3(self):
+                pass
+
+        suite = self.build_test_suite((Tests1, Tests2))
+        subsuite = list(suite)[0]
+        suite.addTest(subsuite)
+        self.assertTestNames(iter_test_cases(suite), expected=[
+            'Tests1.test1', 'Tests2.test2', 'Tests2.test3', 'Tests1.test1',
+        ])
+        reordered_suite = reorder_suite(suite, classes=[])
+        self.assertTestNames(reordered_suite, expected=[
+            'Tests1.test1', 'Tests2.test2', 'Tests2.test3',
+        ])
+        reordered_suite = reorder_suite(suite, classes=[], reverse=True)
+        self.assertTestNames(reordered_suite, expected=[
+            'Tests2.test3', 'Tests2.test2', 'Tests1.test1',
+        ])
+
 
 class DependencyOrderingTests(unittest.TestCase):