diff --git a/Lib/test/test_largefile.py b/Lib/test/test_largefile.py
index b2bec1f..407aba8 100644
--- a/Lib/test/test_largefile.py
+++ b/Lib/test/test_largefile.py
@@ -11,25 +11,6 @@
 import os, struct, stat, sys
 
 
-# only run if the current system support large files
-f = open(test_support.TESTFN, 'wb')
-try:
-    # 2**31 == 2147483648
-    f.seek(2147483649L)
-except (IOError, OverflowError):
-    f.close()
-    os.unlink(test_support.TESTFN)
-    raise test_support.TestSkipped, \
-          "platform does not have largefile support"
-else:
-    f.close()
-
-
-# create >2GB file (2GB = 2147483648 bytes)
-size = 2500000000L
-name = test_support.TESTFN
-
-
 # On Windows this test comsumes large resources; It takes a long time to build
 # the >2GB file and takes >2GB of disk space therefore the resource must be
 # enabled to run this test.  If not, nothing after this line stanza will be
@@ -38,6 +19,28 @@
     test_support.requires(
         'largefile',
         'test requires %s bytes and a long time to run' % str(size))
+else:
+    # Only run if the current filesystem supports large files.
+    # (Skip this test on Windows, since we now always support large files.)
+    f = open(test_support.TESTFN, 'wb')
+    try:
+        # 2**31 == 2147483648
+        f.seek(2147483649L)
+        # Seeking is not enough of a test: you must write and flush, too!
+        f.write("x")
+        f.flush()
+    except (IOError, OverflowError):
+        f.close()
+        os.unlink(test_support.TESTFN)
+        raise test_support.TestSkipped, \
+              "filesystem does not have largefile support"
+    else:
+        f.close()
+
+
+# create >2GB file (2GB = 2147483648 bytes)
+size = 2500000000L
+name = test_support.TESTFN
 
 
 def expect(got_this, expect_this):