1) Don't wear a T-shirt under it, wear an undershirt. An undershirt that fits properly should be tight enough to wear under a polo without the sleeves showing. Choose crew neck or v-neck, depending on whether you want it to show. If the sleeves really are a problem, find undershirts that have smaller sleeves...I haven't worn one in a long time, but I know they exist. If you can't find any, as a last resort, try A-shirts, aka beaters. Although they don't actually cover the armpit area, they're better than doing nothing. 2) Wash the shirt as soon as possible. At a minimum, pretreat otherwise. 3) If stains develop, try oxiclean. I've never done so myself, but I hear that it works wonders. 4) You can bleach that shirt if you want to. If you follow the directions on the bleach, it will not fade the croc. 5) I was under the impression that it's the aluminum in anti-perspirate that actually causes the stains, as opposed to the sweat itself. Try switching to one that doesn't have aluminum, or just use plain deodorant, or use none at all (if that's a feasible/considerate option). Hope this helps.