How to use Python Mock to raise an exception - but with Errno set to a given value

Given this Python code:

elif request.method == 'DELETE':
    try:
        os.remove(full_file)
        return jsonify({'results':'purged %s' % full_file})

    except OSError as e:
        if e.errno != errno.ENOENT:
            raise

        return jsonify({'results':'file not present: %s' % full_file})

I want to test all possible paths, including the exception handling. Using Mock, it's easy enough to raise an exception, which I do with this code:

with patch('os.remove', new=Mock(side_effect=OSError(errno.ENOENT))):
    self.assertRaises(OSError, self.app.delete, file_URL) # broken

Mock raises an exception, which has a printed value of 2 (ENOENT) - but e.errno is set to NONE. And so far, I have not found a way to set it. The result is, the exception always gets re-raised, and I never reach the last line of code, in my unit test.

I've also tried creating a dummy class with errno set, and returning that. But unless it has *side_effect* set to be called, it doesn't raise an exception, and when I set side_effect, I don't get the object.errno as a return value.

Is there a way to have Mock raise an Exception, where that Exception object has the errno attribute set?