CS,
I remember doing this theoreticaly in Uni, so for what it's worth, will add my thoughts.
Efficiency with altitude comes in two parts. Firstly, as you stated, the higher you climb, the greater your TAS - as the atmosphere becomes more rarefied, the aircraft has to travel faster to stay up there! Thus, you are covering more range for unit fuel burn.
The second aspect is that of turbine efficiency. The higher you go, the more efficient the turbine cycle becomes due to the difference in the OAT and the trubine temperature becomeing grater (turbine entry temp stays essentially constant). Thus, you get a greater SPECIFIC thrust due to TSFC (Thrust Specific Fuel Constmption) being greater. However, SPECIFIC thrust is the thrust generated per unit mass flow of air through the engine. As you climb, the mass flow through the engine decreases and thus the thrust drop off. It is stated by some that the "ram effect" of travelling at the higher speed reverses the effect of the lower density - this is not really true as the dynamic pressure id greater flying at lower altitudes.
On that note, what HD said is correct. After the tropopause, the temperature remains constant (hence no further increase in engine efficiency) whilst the density continues to fall. Thus, the point of greatest efficiency is not too far away from the tropopause.
Hope you can de-code my ramblings!
Cuban_8