I recently purchased a pair of Demozu 5 inch Dry Fit running shorts. I'm 6'1", 162 lbs - medium size was a good fit. I had read other reviewers comments regarding the built-in brief and had concerns, but my first run in them was 14 miles, and I didn't think about the comfort of the shorts at all, which meant they were working fine. The only thing I use the zipper pocket for is my car key fob, and it was fine for that, but I don't think I would have wanted anything heavier in there while running.
When I purchased these I was looking for a less expensive alternative to the name brands, so I also bought a pair of Baleaf 5 inch shorts to compare the two. That turns out to be impossible, because the Demozu and the Baleaf are the identical short. The only difference is the brand tag sewed over the fabric tag in the waist band, and the name silk-screened on the left leg (in the exact same spot). Everything else is exactly the same.