diff --git a/Lib/test/test_mailbox.py b/Lib/test/test_mailbox.py
index 0696fef586c..01c4373fade 100644
--- a/Lib/test/test_mailbox.py
+++ b/Lib/test/test_mailbox.py
@@ -146,6 +146,7 @@ class TestMailbox(TestBase):
         msg = self._box.get(key1)
         self.assertEqual(msg['from'], 'foo')
         self.assertEqual(msg.fp.read(), '1' + os.linesep)
+        msg.fp.close()
 
     def test_getitem(self):
         # Retrieve message using __getitem__()
@@ -178,10 +179,14 @@ class TestMailbox(TestBase):
         # Get file representations of messages
         key0 = self._box.add(self._template % 0)
         key1 = self._box.add(_sample_message)
-        self.assertEqual(self._box.get_file(key0).read().replace(os.linesep, '\n'),
+        msg0 = self._box.get_file(key0)
+        self.assertEqual(msg0.read().replace(os.linesep, '\n'),
                          self._template % 0)
-        self.assertEqual(self._box.get_file(key1).read().replace(os.linesep, '\n'),
+        msg1 = self._box.get_file(key1)
+        self.assertEqual(msg1.read().replace(os.linesep, '\n'),
                          _sample_message)
+        msg0.close()
+        msg1.close()
 
     def test_get_file_can_be_closed_twice(self):
         # Issue 11700
@@ -427,6 +432,7 @@ class TestMailbox(TestBase):
         self._box.add(contents[0])
         self._box.add(contents[1])
         self._box.add(contents[2])
+        oldbox = self._box
         method()
         if should_call_close:
             self._box.close()
@@ -435,6 +441,7 @@ class TestMailbox(TestBase):
         self.assertEqual(len(keys), 3)
         for key in keys:
             self.assertIn(self._box.get_string(key), contents)
+        oldbox.close()
 
     def test_dump_message(self):
         # Write message representations to disk
@@ -1968,7 +1975,9 @@ class MaildirTestCase(unittest.TestCase):
         self.createMessage("cur")
         self.mbox = mailbox.Maildir(test_support.TESTFN)
         #self.assertTrue(len(self.mbox.boxes) == 1)
-        self.assertIsNot(self.mbox.next(), None)
+        msg = self.mbox.next()
+        self.assertIsNot(msg, None)
+        msg.fp.close()
         self.assertIs(self.mbox.next(), None)
         self.assertIs(self.mbox.next(), None)
 
@@ -1976,7 +1985,9 @@ class MaildirTestCase(unittest.TestCase):
         self.createMessage("new")
         self.mbox = mailbox.Maildir(test_support.TESTFN)
         #self.assertTrue(len(self.mbox.boxes) == 1)
-        self.assertIsNot(self.mbox.next(), None)
+        msg = self.mbox.next()
+        self.assertIsNot(msg, None)
+        msg.fp.close()
         self.assertIs(self.mbox.next(), None)
         self.assertIs(self.mbox.next(), None)
 
@@ -1985,8 +1996,12 @@ class MaildirTestCase(unittest.TestCase):
         self.createMessage("new")
         self.mbox = mailbox.Maildir(test_support.TESTFN)
         #self.assertTrue(len(self.mbox.boxes) == 2)
-        self.assertIsNot(self.mbox.next(), None)
-        self.assertIsNot(self.mbox.next(), None)
+        msg = self.mbox.next()
+        self.assertIsNot(msg, None)
+        msg.fp.close()
+        msg = self.mbox.next()
+        self.assertIsNot(msg, None)
+        msg.fp.close()
         self.assertIs(self.mbox.next(), None)
         self.assertIs(self.mbox.next(), None)
 
@@ -1995,11 +2010,13 @@ class MaildirTestCase(unittest.TestCase):
         import email.parser
         fname = self.createMessage("cur", True)
         n = 0
-        for msg in mailbox.PortableUnixMailbox(open(fname),
+        fid = open(fname)
+        for msg in mailbox.PortableUnixMailbox(fid,
                                                email.parser.Parser().parse):
             n += 1
             self.assertEqual(msg["subject"], "Simple Test")
             self.assertEqual(len(str(msg)), len(FROM_)+len(DUMMY_MESSAGE))
+        fid.close()
         self.assertEqual(n, 1)
 
 ## End: classes from the original module (for backward compatibility).
diff --git a/Lib/test/test_old_mailbox.py b/Lib/test/test_old_mailbox.py
index e8dff5079b5..14ba9c08631 100644
--- a/Lib/test/test_old_mailbox.py
+++ b/Lib/test/test_old_mailbox.py
@@ -73,7 +73,9 @@ class MaildirTestCase(unittest.TestCase):
         self.createMessage("cur")
         self.mbox = mailbox.Maildir(test_support.TESTFN)
         self.assertTrue(len(self.mbox) == 1)
-        self.assertTrue(self.mbox.next() is not None)
+        msg = self.mbox.next()
+        self.assertTrue(msg is not None)
+        msg.fp.close()
         self.assertTrue(self.mbox.next() is None)
         self.assertTrue(self.mbox.next() is None)
 
@@ -81,7 +83,9 @@ class MaildirTestCase(unittest.TestCase):
         self.createMessage("new")
         self.mbox = mailbox.Maildir(test_support.TESTFN)
         self.assertTrue(len(self.mbox) == 1)
-        self.assertTrue(self.mbox.next() is not None)
+        msg = self.mbox.next()
+        self.assertTrue(msg is not None)
+        msg.fp.close()
         self.assertTrue(self.mbox.next() is None)
         self.assertTrue(self.mbox.next() is None)
 
@@ -90,8 +94,12 @@ class MaildirTestCase(unittest.TestCase):
         self.createMessage("new")
         self.mbox = mailbox.Maildir(test_support.TESTFN)
         self.assertTrue(len(self.mbox) == 2)
-        self.assertTrue(self.mbox.next() is not None)
-        self.assertTrue(self.mbox.next() is not None)
+        msg = self.mbox.next()
+        self.assertTrue(msg is not None)
+        msg.fp.close()
+        msg = self.mbox.next()
+        self.assertTrue(msg is not None)
+        msg.fp.close()
         self.assertTrue(self.mbox.next() is None)
         self.assertTrue(self.mbox.next() is None)
 
diff --git a/Misc/ACKS b/Misc/ACKS
index 958951f0f53..88b7ed03547 100644
--- a/Misc/ACKS
+++ b/Misc/ACKS
@@ -762,6 +762,7 @@ Gavrie Philipson
 Adrian Phillips
 Christopher J. Phoenix
 Neale Pickett
+Matti Picus
 Jim St. Pierre
 Dan Pierson
 Martijn Pieters
diff --git a/Misc/NEWS b/Misc/NEWS
index c5eaa9c966e..5052009e738 100644
--- a/Misc/NEWS
+++ b/Misc/NEWS
@@ -435,6 +435,9 @@ Extension Modules
 Tests
 -----
 
+- Issue #15040: Close files in mailbox tests for PyPy compatibility.
+  Original patch by Matti Picus.
+
 - Issue #15802: Fix test logic in TestMaildir.test_create_tmp. Patch
   by Serhiy Storchaka.