No minimum signal rule, since a translator wouldn't have enough power to throw even a 60 dbu over a large city.
From memory, so I would just go read the rules (47 CFR 74.1201 et seq.):
1. You can move to an adjacent channel.
2. You can move to an IF beat channel (but not if its a commercial translator and the IF beat falls below 92.1)
3. You can change transmitter location, inclrease power, height or change antenna so long as you are covering esssentially the same city of license.
Of course, must meet protections standards, such as they are, of 74.1204.