How are your hands positioned? I ride a drop bar, I find that if I ride with my hands on the top of the bar. The part that comes straight out from the stem, then I'll get some wrist issues. If I ride in the drops or have my hands on the hoods of the shifters, then wrist issues are seldom. Though that does bring up how to properly hold the hoods which when incorrectly done will cause pain in the heel of the palm.
I feel like I lessened the pressure on my hands and wrists by going lower with the bars.