diff --git a/Lib/test/test_dbm.py b/Lib/test/test_dbm.py
index 8fdd262..ed92bfe 100755
--- a/Lib/test/test_dbm.py
+++ b/Lib/test/test_dbm.py
@@ -6,11 +6,11 @@
 import random
 import dbm
 from dbm import error
-from test.test_support import verbose, verify, TestSkipped
+from test.test_support import verbose, verify, TestSkipped, TESTFN
 
 # make filename unique to allow multiple concurrent tests
 # and to minimize the likelihood of a problem from an old file
-filename = '/tmp/delete_me_' + str(random.random())[-6:]
+filename = TESTFN
 
 def cleanup():
     for suffix in ['', '.pag', '.dir', '.db']:
diff --git a/Lib/test/test_gdbm.py b/Lib/test/test_gdbm.py
index e76539a..a689576 100755
--- a/Lib/test/test_gdbm.py
+++ b/Lib/test/test_gdbm.py
@@ -5,9 +5,9 @@
 
 import gdbm
 from gdbm import error
-from test.test_support import verbose, verify, TestFailed
+from test.test_support import verbose, verify, TestFailed, TESTFN
 
-filename= '/tmp/delete_me'
+filename = TESTFN
 
 g = gdbm.open(filename, 'c')
 verify(g.keys() == [])