My rig has a tether which I clip to my left hip D-ring. The tether is fixed to the lower left side of my tray. I've also tied a boltsnap to the top of the right side tray handle. If I'm too busy diving to properly handle my rig, I stow the strobe arms and clip the rig off to one of my shoulder D-rings (usually the left hand D-ring). If i don't have time to prepare, but need both hands for diving I just let go of my rig and let it dangle from its tether while I'm busy diving.
When I used a compact without strobes, I basically did the same. Only difference was, I didn't have to stow the strobe arms before clipping off the rig.