diff --git a/Lib/test/test_dbm_dumb.py b/Lib/test/test_dbm_dumb.py
index 21f29af..652a355 100644
--- a/Lib/test/test_dbm_dumb.py
+++ b/Lib/test/test_dbm_dumb.py
@@ -281,6 +281,21 @@
                 self.assertEqual(sorted(f.keys()), sorted(self._dict))
                 f.close()  # don't write
 
+    @unittest.skipUnless(support.TESTFN_NONASCII,
+                         'requires OS support of non-ASCII encodings')
+    def test_nonascii_filename(self):
+        filename = support.TESTFN_NONASCII
+        for suffix in ['.dir', '.dat', '.bak']:
+            self.addCleanup(support.unlink, filename + suffix)
+        with dumbdbm.open(filename, 'c') as db:
+            db[b'key'] = b'value'
+        self.assertTrue(os.path.exists(filename + '.dat'))
+        self.assertTrue(os.path.exists(filename + '.dir'))
+        with dumbdbm.open(filename, 'r') as db:
+            self.assertEqual(list(db.keys()), [b'key'])
+            self.assertTrue(b'key' in db)
+            self.assertEqual(db[b'key'], b'value')
+
     def tearDown(self):
         _delete_files()
 
diff --git a/Lib/test/test_dbm_gnu.py b/Lib/test/test_dbm_gnu.py
index 304b332..d96df92 100644
--- a/Lib/test/test_dbm_gnu.py
+++ b/Lib/test/test_dbm_gnu.py
@@ -2,7 +2,7 @@
 gdbm = support.import_module("dbm.gnu") #skip if not supported
 import unittest
 import os
-from test.support import TESTFN, unlink
+from test.support import TESTFN, TESTFN_NONASCII, unlink
 
 
 filename = TESTFN
@@ -93,5 +93,39 @@
         self.assertEqual(str(cm.exception),
                          "GDBM object has already been closed")
 
+    def test_bytes(self):
+        with gdbm.open(filename, 'c') as db:
+            db[b'bytes key \xbd'] = b'bytes value \xbd'
+        with gdbm.open(filename, 'r') as db:
+            self.assertEqual(list(db.keys()), [b'bytes key \xbd'])
+            self.assertTrue(b'bytes key \xbd' in db)
+            self.assertEqual(db[b'bytes key \xbd'], b'bytes value \xbd')
+
+    def test_unicode(self):
+        with gdbm.open(filename, 'c') as db:
+            db['Unicode key \U0001f40d'] = 'Unicode value \U0001f40d'
+        with gdbm.open(filename, 'r') as db:
+            self.assertEqual(list(db.keys()), ['Unicode key \U0001f40d'.encode()])
+            self.assertTrue('Unicode key \U0001f40d'.encode() in db)
+            self.assertTrue('Unicode key \U0001f40d' in db)
+            self.assertEqual(db['Unicode key \U0001f40d'.encode()],
+                             'Unicode value \U0001f40d'.encode())
+            self.assertEqual(db['Unicode key \U0001f40d'],
+                             'Unicode value \U0001f40d'.encode())
+
+    @unittest.skipUnless(TESTFN_NONASCII,
+                         'requires OS support of non-ASCII encodings')
+    def test_nonascii_filename(self):
+        filename = TESTFN_NONASCII
+        self.addCleanup(unlink, filename)
+        with gdbm.open(filename, 'c') as db:
+            db[b'key'] = b'value'
+        self.assertTrue(os.path.exists(filename))
+        with gdbm.open(filename, 'r') as db:
+            self.assertEqual(list(db.keys()), [b'key'])
+            self.assertTrue(b'key' in db)
+            self.assertEqual(db[b'key'], b'value')
+
+
 if __name__ == '__main__':
     unittest.main()
diff --git a/Lib/test/test_dbm_ndbm.py b/Lib/test/test_dbm_ndbm.py
index 49f4426..fb7d0e8 100644
--- a/Lib/test/test_dbm_ndbm.py
+++ b/Lib/test/test_dbm_ndbm.py
@@ -1,5 +1,6 @@
 from test import support
 support.import_module("dbm.ndbm") #skip if not supported
+import os
 import unittest
 import dbm.ndbm
 from dbm.ndbm import error
@@ -47,6 +48,42 @@
         self.assertEqual(str(cm.exception),
                          "DBM object has already been closed")
 
+    def test_bytes(self):
+        with dbm.ndbm.open(self.filename, 'c') as db:
+            db[b'bytes key \xbd'] = b'bytes value \xbd'
+        with dbm.ndbm.open(self.filename, 'r') as db:
+            self.assertEqual(list(db.keys()), [b'bytes key \xbd'])
+            self.assertTrue(b'bytes key \xbd' in db)
+            self.assertEqual(db[b'bytes key \xbd'], b'bytes value \xbd')
+
+    def test_unicode(self):
+        with dbm.ndbm.open(self.filename, 'c') as db:
+            db['Unicode key \U0001f40d'] = 'Unicode value \U0001f40d'
+        with dbm.ndbm.open(self.filename, 'r') as db:
+            self.assertEqual(list(db.keys()), ['Unicode key \U0001f40d'.encode()])
+            self.assertTrue('Unicode key \U0001f40d'.encode() in db)
+            self.assertTrue('Unicode key \U0001f40d' in db)
+            self.assertEqual(db['Unicode key \U0001f40d'.encode()],
+                             'Unicode value \U0001f40d'.encode())
+            self.assertEqual(db['Unicode key \U0001f40d'],
+                             'Unicode value \U0001f40d'.encode())
+
+    @unittest.skipUnless(support.TESTFN_NONASCII,
+                         'requires OS support of non-ASCII encodings')
+    def test_nonascii_filename(self):
+        filename = support.TESTFN_NONASCII
+        for suffix in ['', '.pag', '.dir', '.db']:
+            self.addCleanup(support.unlink, filename + suffix)
+        with dbm.ndbm.open(filename, 'c') as db:
+            db[b'key'] = b'value'
+        self.assertTrue(any(os.path.exists(filename + suffix)
+                            for suffix in ['', '.pag', '.dir', '.db']))
+        with dbm.ndbm.open(filename, 'r') as db:
+            self.assertEqual(list(db.keys()), [b'key'])
+            self.assertTrue(b'key' in db)
+            self.assertEqual(db[b'key'], b'value')
+
+
 
 if __name__ == '__main__':
     unittest.main()