Mirroring BitmapData

In an effort to cut down on the filesize of my swf i have only created a tilesheet of my character facing right, with the intention of programmatically mirroring this for the left facing tiles.

I’ve been looking for a way to do this, but so far all i can find is applying a TransformMatrix on the Bitmap. Unfortunately (I am assuming) I need to mirror the actual BitmapData, not the Bitmap, otherwise my CopyPixels will just use the original bitmapData. I know i can do it by literally creating a new BitmapData and then copying the pixels into their new correct place 1 by 1, but this seems like a pretty bad solution.

Anyone got any ideas?