Thanks for the clarification Milt. Please excuse my quoting you in big blocks - normally I hate that, but in this case the page is so long that scrolling up & down is tedious , so using quotes is easier.
We have climbed to a safe height, closed down the left engine, upped the power on the right engine and settled into a steady straight cruise with wings level and found that the rudder is trimmed right foot with about one third deflection. Balance ball is in the centre even though we know we are sideslipping by about 3 degrees. Hard to tell though.
In steady straight wings level flight with the LEFT engine shut down, you will be slipping LEFT with rudder force to the LEFT. Directional stability forces - those tending to make the aircraft yaw into a sideslip - will be to the RIGHT.
We have climbed to a safe height, closed down the left engine and allowed the aircraft to yaw hard left to discover that the angle of Right sideslip is excessive and the rudder has trailed over to left foot. ... There is not enough tail sideforce to the left being produced to get us pointing in the direction close to where we want to go and all of that sideslip is giving us unbalanced lift from the wings so we have to hold level with a fair bit of aileron. Let us ... push in some R foot rudder. Now we have given the tail some help and we have reduced the angle of RIGHT sideslip down to a lower angle so that we are now flying about 2/3 degrees Right of where the aircraft is pointing.
You describe a different situation here: it will not be straight wings level flight! If the wings are level, you'll be turning into the dead engine. If the flightpath is straight, you will be banking into the live engine. Using some R foot rudder to give the tail some help will do as you say, but the wings still won't quite be level, or the aircraft will not quite be keeping straight. Also of course the balance ball won't be centred in this case.
That's the last time I'll quote you - promise! - as I can see the discussion is moving on to other things. I won't clarify what I meant earlier, simply because that marvellous site bookmarked above says it all much better than I can, with pictures too!
cheers,
overcast8