This top was altered by the previous owner, and it fits like a 34GG, so I would say it probably ran true to size. I haven't tried it with the shoulder strap but it stays up just fine without it; I wore it all day as a strapless bra under a dress and it worked fine. (Now that I think on it, better than any actual strapless bra I ever owned.) If I were buying one new, I'd look for a cup size down in the larger of my regular band sizes (i.e. a 32GG) just to get a little less chest coverage. If I weren't short, I wouldn't care because the support is great and I don't need swimwear to be as tight as my bras. Seems beautifully made of excellent materials.
This top doesn't really fit, but it's so cute that I can't pass it on. The band was altered by the previous owner and I thought it would fit more like a 34GG or 32H, but it must run small in the cup. It's also a little wide & shallow, so it has a somewhat flattening effect. I know, it doesn't sound attractive. But it is a cute set, and my standards for fit are much more flexible on swimwear than for undergarments. It doesn't have some of the higher-end construction details that I've grown accustomed to (i.e. inner slings, lining, vertical seaming, fancier hardware, etc.), but it seems sturdily made.