I am a small-band, large-cup person (34K, UK sizes) and two of my top-4 have been listed above -- Shock Absorber and Panache. They are actually 3 & 4 on my list, which isn't a knock on their quality, just a commentary on how they fit and work FOR ME. They are absolutely worth trying.
My top 2 are Freya Active (runs about a cup size small in my experience, and you may need to go up a band size because the bands are VERY snug) and the Elomi Energise. The Energise is, I think, an AMAZING bra. I'm a gardener so I bought it initially planning for it to be a work bra -- would hold up to sweat, and it wouldn't give me uniboob (it's underwired and encapsulating). I tried it while running just to see how it was, and it's FANTASTIC, with really good bounce control, and also a fantastic everyday bra. I now own 6 of them and they're what I wear 5-6 days of the week. I can be dressed for a meeting and look as if I'm wearing a regular bra, and yet still chase my dog down the street without bouncing out of my top. The only issues with it are that it comes up high on the chest, so I can't wear it with v-necks (most scoopnecks are fine).
