Timing for rocket jumping?

[The Professional Amateur]

I've beaten most of the game by this point, but the Helladeck is stumping me due to one of the levels requiring rocket jumping with Jeff, and I just can't figure out how to. Should I be pressing jump just as I fire? Before? After? I just can't seem to get it right, though I do sometimes see the blast slightly slow my fall during a short jump. On the off chance anyone's still around, care to give me some pointers?

[Auspice]

You want to be as close to the rocket's center as possible and airborne. So release as early as possible after jumping.