Contacttower I can't answer that I'm afraid; I'm currently operating the Dash 8 so Bob would be the one to ask, or have a look through Handling the Big Jets, a very informative read.
In normal operations we fly at 20000 or less and have no problems with aircraft controllability, although I understand at high altitudes passenger jets suffer from a lack of damping due the thin air.
Our Minimum Equipment List allows us to depart no Autopilot and no Flight Director, the MEL is set by the manufacturer. I have no idea what the dispatch requirements would be for a Boeing or Airbus type, but bottom line the crew have to be able to cope with a failure of the Autopilot or/and the Flight Director.