Always try to delete the data file before and after the test.
This will hopefully avoid spurious failures if the file doesn't
have the proper permissions to write for some reason.
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)