I can't imagine not wearing an undershirt. Well, I can, but not with a white shirt that would develop antiperspirant stains in short order. Would much rather see a dude's undershirt peeking out than big circles of sweat under his arms. If its stains you worry about, then switch to a non aluminum based deodorant. Contrary to popular belief it is often the over use of anti-perspirant, that causes excessive production of sweat.