On Engine Out Operation in Boeing Airplanes, which altitude is preferable, the OPT Altitude, the MAX Altitude or the RECOM Altitude of the ENG OUT CRZ Page?
You'd typically drift down to your max single-engine altitude, which means essentially that max continuous power on the operating engine is sufficient for level flight at that altitude. Higher than that, you have a slow descent going in order for the thrust you have to maintain the recommended driftdown airspeed.
In general, there wouldn't be any advantage to descending lower than this until you need to do so for approach and landing, so you'd probably remain at that max altitude. As you burn off fuel, your max engine-out altitude would slowly increase so (hypothetically) you could actually step-climb up a little bit if you were going to be at that new Single Engine cruise altitude long enough, but in practice you'd need to lose the engine a LONG way from landing before the idea of step-climbing up to a higher SE cruise altitude would make practical sense.
The "Max" altitude is only reachable with the thrust of 2 engines, and the "OPT" altitude is probably well above what your max SE altitude is anyway -- it's optimum for cruising with both engines operating, after all. Granted, a sufficiently high Cost Index and/or strange winds can pull the Optimum altitude down, but in 99% of the cases, Optimum is going to be well above Max Single Engine altitude.