FBinNY 

Pour coffee over both 1/2 hour before riding.

As mentioned above, hand/arm alignment is usually the issue.

Hold your arm out in front you and note how your relaxed hand is aligned with the arm. Holding the wrist bent either backward or to wither side can pinch the nerves in the carpal tunnel, or restrict circulation, and lead to the tingling or "falling asleep" effects you describe.

So, now look at your position on the bike. If your hand and arm aren't aligned naturally, rotate the bars up or down to find a more natural alignment in your normal grip position. Test it this way by riding a few days before considering it final, then you can move the brake levers and rotate the bar to get the most utility in the most positions.

BTW- I'm hearing more of this issue these days, and suspect that it's because many people are riding the brake hoods and gripping the lever body. If you're one of those, and like riding the hoods, consider relaxing and hanging your hands over supported my the thumb arch, with the fingers extending forward rather than wrapped around the lever body. This is a relaxed grip, and secure because gravity keeps your hands positioned.