Unfortunately this project was on a previous laptop so I'm piecing together pieces to try and recreate what I did.
I misspoke, for this particular one I can see that I used Ditherer to get it down to 16 from the original image (attached). However for the life of me I can't seem to recreate the image exactly, although it is awfully close. ATK cubed does get me the closest match.
I know that I've converted images to only use colors that are available in TM before taking the dithering step and have also reduced the number of colors to 64/48/32 if I don't like the result that I'm getting.
Byfield.bmp