diff --git a/Lib/test/test_codecs.py b/Lib/test/test_codecs.py
index 47b80f7..52e8dc9 100644
--- a/Lib/test/test_codecs.py
+++ b/Lib/test/test_codecs.py
@@ -1490,7 +1490,7 @@
 
 class BomTest(unittest.TestCase):
     def test_seek0(self):
-        data = "1234567890"
+        data = u"1234567890"
         tests = ("utf-16",
                  "utf-16-le",
                  "utf-16-be",
@@ -1498,8 +1498,8 @@
                  "utf-32-le",
                  "utf-32-be")
         for encoding in tests:
-            with codecs.open('foo', 'wt+', encoding=encoding) as f:
-                # Check if the BOM is written only once
+            # Check if the BOM is written only once
+            with codecs.open(test_support.TESTFN, 'w+', encoding=encoding) as f:
                 f.write(data)
                 f.write(data)
                 f.seek(0)
@@ -1507,6 +1507,42 @@
                 f.seek(0)
                 self.assertEquals(f.read(), data * 2)
 
+            # Check that the BOM is written after a seek(0)
+            with codecs.open(test_support.TESTFN, 'w+', encoding=encoding) as f:
+                f.write(data[0])
+                self.assertNotEquals(f.tell(), 0)
+                f.seek(0)
+                f.write(data)
+                f.seek(0)
+                self.assertEquals(f.read(), data)
+
+            # (StreamWriter) Check that the BOM is written after a seek(0)
+            with codecs.open(test_support.TESTFN, 'w+', encoding=encoding) as f:
+                f.writer.write(data[0])
+                self.assertNotEquals(f.writer.tell(), 0)
+                f.writer.seek(0)
+                f.writer.write(data)
+                f.seek(0)
+                self.assertEquals(f.read(), data)
+
+            # Check that the BOM is not written after a seek() at a position
+            # different than the start
+            with codecs.open(test_support.TESTFN, 'w+', encoding=encoding) as f:
+                f.write(data)
+                f.seek(f.tell())
+                f.write(data)
+                f.seek(0)
+                self.assertEquals(f.read(), data * 2)
+
+            # (StreamWriter) Check that the BOM is not written after a seek()
+            # at a position different than the start
+            with codecs.open(test_support.TESTFN, 'w+', encoding=encoding) as f:
+                f.writer.write(data)
+                f.writer.seek(f.writer.tell())
+                f.writer.write(data)
+                f.seek(0)
+                self.assertEquals(f.read(), data * 2)
+
 
 def test_main():
     test_support.run_unittest(