Yeah, speed is good. Polishing compound on a stitched cotton buffing wheel - red then white - then mother's on a loose cotton wheel. Also, if you sand to 2500 grit, you might try going over that again with 3000. I find 3k is a bit closer to the polishing compound... actually I can barely tell the difference between 3000 and black compound. Of course, compound doesn't leave sanding marks.
The video in the link below is only slightly unrelated. The first half of it is all about polishing, granted it's a different method and material, but the concept is the same.