I have DSL now, but back when I had 56k, WCIII ran pretty well, little lag and few disconnects. But, I had most of the detail settings pretty low, if that affects it at all. Still, a 56k should have no problem with WCIII, but you mught want to stick to 1v1, 2v2 and FFA, to be on the safe side. Bigger games ought to run ok, but, when I had 56k, heavy lag and disconnects were much more frequent in those larger games, though still not common.