diff -r 60163fc72017 Lib/tarfile.py
--- a/Lib/tarfile.py	Mon Jan 13 13:51:42 2014 -0500
+++ b/Lib/tarfile.py	Mon Jan 13 21:58:43 2014 +0200
@@ -1603,21 +1603,24 @@
         except (ImportError, AttributeError):
             raise CompressionError("gzip module is not available")
 
-        extfileobj = fileobj is not None
         try:
             fileobj = gzip.GzipFile(name, mode + "b", compresslevel, fileobj)
+        except OSError:
+            if fileobj is not None and mode == 'r':
+                raise ReadError("not a gzip file")
+            raise
+
+        try:
             t = cls.taropen(name, mode, fileobj, **kwargs)
         except OSError:
-            if not extfileobj and fileobj is not None:
-                fileobj.close()
-            if fileobj is None:
-                raise
-            raise ReadError("not a gzip file")
+            fileobj.close()
+            if mode == 'r':
+                raise ReadError("not a gzip file")
+            raise
         except:
-            if not extfileobj and fileobj is not None:
-                fileobj.close()
+            fileobj.close()
             raise
-        t._extfileobj = extfileobj
+        t._extfileobj = False
         return t
 
     @classmethod
@@ -1640,7 +1643,9 @@
             t = cls.taropen(name, mode, fileobj, **kwargs)
         except (OSError, EOFError):
             fileobj.close()
-            raise ReadError("not a bzip2 file")
+            if mode == 'r':
+                raise ReadError("not a bzip2 file")
+            raise
         t._extfileobj = False
         return t
 
@@ -1663,7 +1668,9 @@
             t = cls.taropen(name, mode, fileobj, **kwargs)
         except (lzma.LZMAError, EOFError):
             fileobj.close()
-            raise ReadError("not an lzma file")
+            if mode == 'r':
+                raise ReadError("not an lzma file")
+            raise
         t._extfileobj = False
         return t
 
diff -r 60163fc72017 Lib/test/test_tarfile.py
--- a/Lib/test/test_tarfile.py	Mon Jan 13 13:51:42 2014 -0500
+++ b/Lib/test/test_tarfile.py	Mon Jan 13 21:58:43 2014 +0200
@@ -1137,6 +1137,22 @@
         finally:
             os.chdir(cwd)
 
+    def test_open_nonwritable_fileobj(self):
+        for exctype in OSError, EOFError, RuntimeError:
+            class BadFile(io.BytesIO):
+                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 GzipWriteTest(GzipTest, WriteTest):
     pass