you may be more likely to puncture at street pressures as the tires wont flex around the rocks as much as they will aired down. Id go down to maybe 20PSI as a starting point and see how it goes, you can always take more out or put more in.
92 YJ. High Output 4.0L
Rubicon Express 4" Lift Kit, 2" Body Lift,15x8" AR 767s, 35x12.50 Xterrains, Home Made Snorkel, Sanden OBA, Home made rocker gaurds. 8.8 Rear with Discs, 4.10s F&R, ARB rear, Detroit EZ Locker front, WarnM8000 with Viking Synthetic Line, Beadlocks, Tons of Mods
My RigRater Score: 682RRv1.0 with a BOA of 13.47
I'm now doing custom bumpers and lift installs in So-cal
I wheeled many times before without airing down and never popped a tire, its all about being careful and picking good lines. I have noticed that it does make a big difference though if you air down, I was amazed at how much more grip I felt on the trail. I bought a small portable compressor that plugs into the cigarette outlet for filling back up after the trail.
1998 TJ Sport 4.0L 5spd
33x12.5x15 Goodyear Duratracs
Monstaliner, CB, Aux lights my TJ build
IAFF Local 4942
Definitely air down. On all-terrains with no beadlocks, I think 15-20 psi is about right to give you some resistance to blowing the bead and not compromise your ride height too far. Not only will it help your level of grip, but also level of comfort off-road. A tire at 15psi absorbs a lot more of the impact from every single bump. If I might make a recommendation, the MV-50/MF-1050 air compressor (usually $60 or so) is an excellent budget compressor that will refill your tires in about 2 minutes each when you are done for the day. It draws 30 amps and connects straight to the battery with spring clamps.