While not purely strapless, you should still check out Lord & Taylor and the La Blanca "Hola Ombre" Bandeau Halter Tankini top, in tropical pink and orange with a center wooden ring and brown halter strap that ties around the neck.
Instead, the top portion of the tankini is outfitted in a sunny, striped collage of light blue, orange and grey, while the bottom portion of the tankini (the part that sits just under the breastbone) is encased in a deep mid-tone pink.
It is possible for an apron tankini to feature a soft cup bra system that is slightly padded, but if you need to feel more secure or you require a little "oomph" up above, then the apron may not be able to supply the support you need.
For example, the Island Fever S.O.S Tankini is slightly asymmetrical in cut, a look that is quite flattering to the upper portion of your body, but the best part is that it doesn't even show the slightest hint of cleavage.
A great matching set: While it is possible to purchase a tankini top and bottom separately, there is a certain amount of comfort in knowing that you can throw on a perfectly matching set whenever the occasion calls for it.