john lucas
>Steve it depends on how thick your finish is. My experience on furniture was that if I had a high build finish the final steps didn't matter on direction because all you were doing was polishing the finish. If you have a low build that still shows the pores then following the grain is important.

So to answer your question, I think if you are trying for a perfectly glass smooth finish the final polishing steps shouldn't matter if you follow the grain. I have limited experience with this on turnings because I seldom do this kind of finish but the above holds true for what I've done.