I was actually a bit surprised to learn how snug a properly fitted bra should be; I am 39" underbust, but the fitter immediately said I should be in a 38 band, and then she reassured me that it really should feel that "tight" at first. She was right - the support was amazing, and it rapidly became more comfortable. She also explained that, contrary to popular belief, the majority of support is provided by the band; if it isn't fitted well, the bra will not be that useful, even if the cups and straps are perfect. I guess that's how strapless bras work.
(I ended up being fitted as a 38DD even though I'd been wearing a 42D in my favorite bra... and even now that I've added one more cup size, I still love the style of bra that the fitter recommended. Annoyingly, though, the 40DD had MUCH bigger cups than the 38DDD, even though they're *supposed* to be the same cup volume. I had to return the 40DD bras.)