The current Lycoming guidance for twins is to use mixture above 3000 agl and throttle below 3000 agl. This seems to work OK, the justification is simple: using mixture is less stressful for the engine but below 3000 agl the stress level on the pilot could be raised to an unacceptable level :-)
For singles the only time I deliberately shut down the engine is as a required part of an aerobatic course. It's done using mixture, above 3000 agl, VMC, within range of good fields.