I learned this tip for fixing red eyes during my summer internship in prepress during my college years. This technique works great for me, and I haven't ever had to search for another way.
1. Zoom in on the eye area of your photo.
2. Using the sponge tool, adjust your brush size to the approximate size of the pupils you are trying to fix. (Just a standard, hard round brush is all you need.)
3. Set your flow to about 50% (this may be the default, I'm not sure).
4. Click several times on each pupil until the redness disappears.
5. TA-DAH! No more red eyes!!
How easy is that?! Hope it works as well for you as it does for me.