Clothes/gear help

[1_2_suckerpunch]

Okay compatriots, I need some help. I am desperately seeking a shirt to go under my dobok, since the neckline plunges far into boob territory. Currently I wear a white t-shirt, but the sleeves ride up, the sides are too baggy, and it takes some adjusting during class. So I'm looking for a sleeveless, more well-fitted one. All the workout shirts I have been able to find are either too low-cut (I need to be able to do pushups without falling out/flashing someone!), too see-through (yes it's an undershirt, but that defeats the purpose), or FAR FAR FAR too expensive.

My criteria are as follows:
-No sleeves...strap vs cut-off sleeve doesn't matter
-Not see-through
-White
-Material doesn't matter. Cotton, lycra, blends, whatever.
-Coverage is the issue, not support. Built-in bras are great, but totally not necessary.

Any ideas or experiences? Thanks!