Someone posted awhile back a type of plane which works best on strips.
Steve,
I think it was John M. who recommended a finger plane. His pix looked like the one sold by General Tools. Ditto everything Russ said. If you're using a sharp low angle block plane even pretty wild grain shouldn't be giving you this kind of problem. People have wrote volumes on the subject of planes. Go to the URL below and enter the Fine Woodworking site. Use its Magazine Index to search "Planes." You'll get about 500 hits. Look them over. I don't have all twenty-five years of back issues, but if you see something you like to look at, and I have it, I can fax it to you. If you're new to woodworking you also might like to check out some of the books offered on this site.
Geo.