Thanks for all the suggestions. I don't wear gloves. I tried them, but felt they made me feel disconnected with the bike. I do wear gloves on my mtn bike, though. Something about the smaller, tighter grip of the hoods and bars make me feel less secure with Gloves. I'll give them another try, though, if they might help.
As for pressure on my hands and nerve compression, I think that has more to do with it, though. I notice a really red patch on the outer fatty part of my palm, on the pinky side of my hand, closer to the wrist. This seems to be where all the pressure is. I just don't know exact movements to reduce the pressure, and I'm fairly certain red spots on your hands while riding isn't normal. I do move my hands around on the bars regularly, too. A local bike shop, from what I've heard from numerous sources, has a very good bike fitter that is certified through Specialized. He supposedly is a miracle worker. He charges $300 for a full bike fit, and I've hesitated to pay that. If I can't resolve this on my own, though, I may need to.