FWIW, I have found that one can reduce the power needed to maintain level flight in a "one-engine out" situation considerably by banking slightly toward the operating engine.
My understanding is the following: When the rudder is deflected to keep the aircraft flying straight with level wings, a side force is generated by the tail that will cause the aircraft to sideslip. This is a very efficient method to reduce performance a lot!
Banking slightly toward the operating engine will incline the lift vector (from the live engine), creating a side force that offsets the one produced by the fin. Once these two forces are equal and opposite the aircraft will no longer slip. Drag will be reduced less engine power is needed.
The explanation may be "hand-waving" but it works for me and I suppose some aerodynamically versed person could explain why it works a lot better than I can.

/Red B.