A 34HH is a 34 band with an HH cup — a very deep, hard-to-find cup. The band does most of the work (around 80% of your support), so if it rides up at the back or the straps dig in, it's the band to fix, not you.
We cut 34HH for fuller busts, part of our full 34D–34K range. Not sure 34HH is your size? Book a personalized fitting and we'll get it sorted.