In terms of efficiency, a turbojet (or turbofan) engine is most efficient at high RPM's. Typically about 90% of it's rated speed. Operating a turbine engine at very low RPM's is a very inefficient way to operate the engine.
The question really isn't about how to make a more efficient idle, but how to burn less fuel. This can only be accomplished by putting less fuel through the engine, which means a lower total fuel burn, lower temperature, lower flame pressure, lower thrust output, paradoxically lower efficiency, and a greater susceptability to flame-out, as well as longer response times, higher thermal transients, etc. Let's not forget that idle settings are also part of the design and measurement of thermal cycles on the engine, and tied not only to operational issues but to maintenance issues involving the cooling and expansion of internal components, to say nothing of the other primary issue noted by Rainboe, which is that the engine is still driving numerous accessories, as well as maintaining a minimum speed for the output of bleed air.
Simply idling it back farther than the manufacturer has originally intended isn't as easy as it seems, nor necessarily a good idea.
The reason we fly higher isn't just for an increase in true airspeed...it's because at higher altitudes we are able to push the power up farther and operate the engine at higher RPM's than at lower altitudes...putting the engine closer to it's most efficient range.