This Ozark light stayed on tight. That was one of the negatives that popped up on a few reviews. It doesn't fit the OP's requirement of not protruding but it sure seems like a viable budget light.
I forgot to turn the GoPro on while shooting these initial shots... But I shot 4 shots from 3 different mags at the little green square from 10 yards. 2 hand grip, just standing. Center to center the group measured 0.62" and that translates to 1.56" at 25 yards. That is in my wheel house when I have targets I can see indoors at that distance (bad lighting in this place for that) so the calculations seem to be representative, at least for me. Bottom two shots on the target were the first pass at 1 shot, reload, 1 shot. I hadn't done that drill with the red dot.
The raw stats about these SP-01 Compacts just can't explain why I love both of mine... How the feel, how they shoot, their reliability, and the roles I am finding for them just make sense. Anyway, didn't mean to detract from the OP's main question. Just sharing the results of this budget light's maiden range trip.