Here in the Maldives, have been asked many times about underwater photography and how to improve shots. A lot of those asking the questions had compacts, and thought to get decent shots they had to upgrade to a DSLR, but after looking at their pics, in nearly every single case they were getting lousy shots for two reasons:
1: They were shooting from too far away.
2: All their shots were taken downwards.
From the various underwater photography courses I have been on and from talking to photo pros, the two biggest changes people can make to improve their UW shots is:
1: Get close, then get closer. You want to be as close as possible to your subject.
2: Shoot level or, preferably, slightly upwards, never downwards.
Do both these basics while shooting underwater and you will notice a major difference in your shots, but to really make a difference, consider an underwater photography course with the likes of Martin Edge, Stuart Philpott (see the April issue of Sport Diver) or Maria Munn.
Cheers
Mark

Get a camera with a decent manual white balance and a separate flash, that's how I get the best results... Although your point about not shooting down into the abyss is spot on.