Issue #20243: TarFile no longer raise ReadError when opened in write mode.
diff --git a/Lib/tarfile.py b/Lib/tarfile.py
index 8a69988..6c40cb9 100755
--- a/Lib/tarfile.py
+++ b/Lib/tarfile.py
@@ -1628,19 +1628,22 @@
         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 IOError:
-            if not extfileobj and fileobj is not None:
-                fileobj.close()
-            if fileobj is None:
-                raise
-            raise ReadError("not a gzip file")
+        except OSError:
+            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 = False
         return t
@@ -1665,7 +1668,9 @@
             t = cls.taropen(name, mode, fileobj, **kwargs)
         except (IOError, EOFError):
             fileobj.close()
-            raise ReadError("not a bzip2 file")
+            if mode == 'r':
+                raise ReadError("not a bzip2 file")
+            raise
         t._extfileobj = False
         return t
 
@@ -1688,7 +1693,9 @@
             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