Ron,

I have done fine with just taking a single pass at a slight angle across the grain with clear band-milled timber.

If you don't want plane marks, my route has been to plane a single pass to remove the saw marks, then sand the timber with either a belt or orbital sander, whatever is on hand. Orbital takes a little longer, but gives a nicer finish. Belt sanders can dig in or leave a bit of a wobbly texture.
The sander doesn't have to do much, just knock of the ridges left by the hand plane. Alternately, you can even use a stiff scraper to knock off the ridges (or as was suggested above, a spokeshave)

I have an upcoming project where I will have to smooth a lot of circular milled hardwood timbers (oak, elm, ash, walnut, hickory, maple, tulip poplar) from a 100+ year old barn. So I've really been thinking about my approach to planing HARD timber lately