Lucky strike! Boeing Flt Ops Tech Bulletin 737-300/400/500 97-1 Dated April 29, 1997. ATA Number 22-31 Subject Autothrottle Operation. from Flt Crew Training PO Box 3707, Seattle.
Precised: First stage is to within 8% of target N1, then to target. THEN (and only then) pilots should adjust to +1% -0% of target. Avoid applying force to the levers unless manual intervention is intended. It also recommends NOT 'following' the levers such that you apply more than 1.5 lbs of force at the top or you may cause the clutch to malfunction. There is a 'caution' that more than 20kts of headwind may produce throttle hold before target is reached.
I always maintain the autothrottle should be allowed to TRY to set power or you may never know when it is malfunctioning.