Strapless at HH cup asks a lot of a bra, and we are honest that the range is limited: only a handful of styles are built to hold this size without straps. Those that do rely on a very firm band, deep multi-section cups and substantial silicone grip.
Fitting a strapless bra at HH cup
Band firmness matters more than anything else. Buy on the tightest hook so there is room to move outward as the elastic relaxes. The cup should contain the bust completely with no spillage at the top edge, since there is no strap to correct a cup that is fractionally too shallow.
Also worth knowing
If a fully strapless bra is not working for you, a multiway style worn with a clear or single strap is a practical alternative — see multiway bras, or the full strapless bra range.