I think it's true to say that throttling one turbine engine back is a waste of time/fuel and much worse than shutting it down! The fuel burn consumed to run an engine providing very little thrust or torque makes it so.
Turbine powered helicopters are very badly affected. In the OEI case, the main gearbox is usually torque limited due to assymetric loading and the maximum speed may therefore be as little as 60% of the twin engined case. This can result in the need for an early diversion for lack of fuel, depending on wind velocity.
Keithl has given the big clue, shutting down a turbine and operating the remaining engine/s at a higher output (more fuel efficient regime) gives a greater ENDURANCE but not necessarily greater RANGE.
It's those (Air) miles per pound that count, not time flown per pound when it comes to getting where you need to go (rather than loitering where you are for longer).
