Off road tire pressure (for rocks)

[RuggedH2]

Anybody want to let me in on the off road pressure they feel comfortable with for rocks?

I have Toyo M/T 35's. As you can see, the tires have much "play" left in them. I have run from 20 psi all the way down to 15 for rocks.

I want to go lower pressure for the traction, but obviously don't want the beads popping. Does anybody here run lower pressure than 15 on the stock H3 wheels, with success? My friends with Jeeps routinely run 10-12 psi, but those rigs don't weigh what we weigh.

Thoughts?