diff --git a/Lib/test/test_tempfile.py b/Lib/test/test_tempfile.py
index 0f514c2..d62b6b5 100644
--- a/Lib/test/test_tempfile.py
+++ b/Lib/test/test_tempfile.py
@@ -7,6 +7,7 @@ import signal
 import sys
 import re
 import warnings
+import contextlib
 
 import unittest
 from test import support
@@ -255,6 +256,16 @@ class TestGetCandidateNames(BaseTestCase):
         self.assertTrue(a is b)
 
 
+@contextlib.contextmanager
+def _inside_empty_temp_dir():
+    dir = tempfile.mkdtemp()
+    try:
+        with support.swap_attr(tempfile, 'tempdir', dir):
+            yield
+    finally:
+        support.rmtree(dir)
+
+
 class TestMkstempInner(BaseTestCase):
     """Test the internal function _mkstemp_inner."""
 
@@ -373,31 +384,49 @@ class TestMkstempInner(BaseTestCase):
         os.lseek(f.fd, 0, os.SEEK_SET)
         self.assertEqual(os.read(f.fd, 20), b"blat")
 
+    def test_collision_with_existing_file(self):
+        # _mkstemp_inner tries another name when a file with
+        # the chosen name already exists
+        with _inside_empty_temp_dir():
+            def mock_get_candidate_names():
+                return iter(['aaa', 'aaa', 'bbb'])
+            with support.swap_attr(tempfile,
+                                   '_get_candidate_names',
+                                   mock_get_candidate_names):
+                flags = tempfile._bin_openflags
+                (fd1, name1) = tempfile._mkstemp_inner(tempfile.gettempdir(),
+                                                      tempfile.template,
+                                                      '',
+                                                      flags)
+                os.close(fd1)
+                self.assertTrue(name1.endswith('aaa'))
+
+                (fd2, name2) = tempfile._mkstemp_inner(tempfile.gettempdir(),
+                                                       tempfile.template,
+                                                       '',
+                                                       flags)
+                os.close(fd2)
+                self.assertTrue(name2.endswith('bbb'))
+
     def test_collision_with_existing_directory(self):
         # _mkstemp_inner tries another name when a directory with
         # the chosen name already exists
-        container_dir = tempfile.mkdtemp()
-        try:
+        with _inside_empty_temp_dir():
             def mock_get_candidate_names():
                 return iter(['aaa', 'aaa', 'bbb'])
             with support.swap_attr(tempfile,
                                    '_get_candidate_names',
                                    mock_get_candidate_names):
-                dir = tempfile.mkdtemp(dir=container_dir)
+                dir = tempfile.mkdtemp()
                 self.assertTrue(dir.endswith('aaa'))
 
                 flags = tempfile._bin_openflags
-                (fd, name) = tempfile._mkstemp_inner(container_dir,
+                (fd, name) = tempfile._mkstemp_inner(tempfile.gettempdir(),
                                                      tempfile.template,
                                                      '',
                                                      flags)
-                try:
-                    self.assertTrue(name.endswith('bbb'))
-                finally:
-                    os.close(fd)
-                    os.unlink(name)
-        finally:
-            support.rmtree(container_dir)
+                os.close(fd)
+                self.assertTrue(name.endswith('bbb'))
 
 
 class TestGetTempPrefix(BaseTestCase):
@@ -554,6 +583,35 @@ class TestMkdtemp(BaseTestCase):
         finally:
             os.rmdir(dir)
 
+    def test_collision_with_existing_file(self):
+        # mkdtemp tries another name when a file with
+        # the chosen name already exists
+        with _inside_empty_temp_dir():
+            def mock_get_candidate_names():
+                return iter(['aaa', 'aaa', 'bbb'])
+            with support.swap_attr(tempfile,
+                                   '_get_candidate_names',
+                                   mock_get_candidate_names):
+                file = tempfile.NamedTemporaryFile(delete=False)
+                file.close()
+                self.assertTrue(file.name.endswith('aaa'))
+                dir = tempfile.mkdtemp()
+                self.assertTrue(dir.endswith('bbb'))
+
+    def test_collision_with_existing_directory(self):
+        # mkdtemp tries another name when a directory with
+        # the chosen name already exists
+        with _inside_empty_temp_dir():
+            def mock_get_candidate_names():
+                return iter(['aaa', 'aaa', 'bbb'])
+            with support.swap_attr(tempfile,
+                                   '_get_candidate_names',
+                                   mock_get_candidate_names):
+                dir1 = tempfile.mkdtemp()
+                self.assertTrue(dir1.endswith('aaa'))
+                dir2 = tempfile.mkdtemp()
+                self.assertTrue(dir2.endswith('bbb'))
+
 
 class TestMktemp(BaseTestCase):
     """Test mktemp()."""