diff --git a/Lib/mailbox.py b/Lib/mailbox.py
index 9978359..a9d9c28 100644
--- a/Lib/mailbox.py
+++ b/Lib/mailbox.py
@@ -1854,7 +1854,10 @@
 
     def close(self):
         """Close the file."""
-        del self._file
+        if hasattr(self, '_file'):
+            if hasattr(self._file, 'close'):
+                self._file.close()
+            del self._file
 
     def _read(self, size, read_method):
         """Read size bytes using read_method."""
@@ -1898,6 +1901,12 @@
             size = remaining
         return _ProxyFile._read(self, size, read_method)
 
+    def close(self):
+        # do *not* close the underlying file object for partial files,
+        # since it's global to the mailbox object
+        if hasattr(self, '_file'):
+            del self._file
+
 
 def _lock_file(f, dotlock=True):
     """Lock file f using lockf and dot locking."""