An H cup one-piece has to be built like a bra with a swimsuit attached, not the other way around. The cup needs enough depth and structure to contain the bust while wet, and the band has to take the load without riding up.
What to look for at H cup
Underwired, encapsulated cups are non-negotiable at this size. Look for a hook-and-eye or otherwise adjustable back, side support panels, and straps set wide enough on the shoulder that they do not slide.
Brands
Elomi Swim is the most reliable at H cup and above, with Panache Swim close behind. Browse all H cup swimwear for the full cup range, or every one-piece swimsuit.
