diff --git a/Lib/tarfile.py b/Lib/tarfile.py
index dd8a142..57ea877 100644
--- a/Lib/tarfile.py
+++ b/Lib/tarfile.py
@@ -1726,7 +1726,9 @@
                 gzip.GzipFile(name, mode, compresslevel, fileobj),
                 **kwargs)
         except IOError:
-            raise ReadError("not a gzip file")
+            if mode == 'r':
+                raise ReadError("not a gzip file")
+            raise
         t._extfileobj = False
         return t
 
@@ -1751,7 +1753,9 @@
         try:
             t = cls.taropen(name, mode, fileobj, **kwargs)
         except (IOError, EOFError):
-            raise ReadError("not a bzip2 file")
+            if mode == 'r':
+                raise ReadError("not a bzip2 file")
+            raise
         t._extfileobj = False
         return t
 
diff --git a/Lib/test/test_tarfile.py b/Lib/test/test_tarfile.py
index 8767d51..e817f61 100644
--- a/Lib/test/test_tarfile.py
+++ b/Lib/test/test_tarfile.py
@@ -979,6 +979,22 @@
             os.unlink(temparchive)
             shutil.rmtree(tempdir)
 
+    def test_open_nonwritable_fileobj(self):
+        for exctype in IOError, EOFError, RuntimeError:
+            class BadFile(StringIO.StringIO):
+                first = True
+                def write(self, data):
+                    if self.first:
+                        self.first = False
+                        raise exctype
+
+            f = BadFile()
+            with self.assertRaises(exctype):
+                tar = tarfile.open(tmpname, self.mode, fileobj=f,
+                                   format=tarfile.PAX_FORMAT,
+                                   pax_headers={'non': 'empty'})
+            self.assertFalse(f.closed)
+
 class StreamWriteTest(WriteTestBase):
 
     mode = "w|"