diff --git a/Lib/test/test_gzip.py b/Lib/test/test_gzip.py
index 08f7f3f..0010112 100644
--- a/Lib/test/test_gzip.py
+++ b/Lib/test/test_gzip.py
@@ -25,13 +25,10 @@
     filename = test_support.TESTFN
 
     def setUp (self):
-        pass
+        test_support.unlink(self.filename)
 
     def tearDown (self):
-        try:
-            os.unlink(self.filename)
-        except os.error:
-            pass
+        test_support.unlink(self.filename)
 
 
     def test_write (self):
diff --git a/Lib/test/test_io.py b/Lib/test/test_io.py
index 513e1f3..f0e79312 100644
--- a/Lib/test/test_io.py
+++ b/Lib/test/test_io.py
@@ -79,6 +79,9 @@
 
 class IOTest(unittest.TestCase):
 
+    def setUp(self):
+        test_support.unlink(test_support.TESTFN)
+
     def tearDown(self):
         test_support.unlink(test_support.TESTFN)
 
@@ -619,6 +622,7 @@
     def setUp(self):
         self.testdata = b"AAA\r\nBBB\rCCC\r\nDDD\nEEE\r\n"
         self.normalized = b"AAA\nBBB\nCCC\nDDD\nEEE\n".decode("ascii")
+        test_support.unlink(test_support.TESTFN)
 
     def tearDown(self):
         test_support.unlink(test_support.TESTFN)