"especially efficient" is correct and usable in written English.
You can use it to emphasize how efficient someone or something is. For example, "The new employee is especially efficient in completing tasks."
Especially efficient as a vehicle for nostalgia is the Facebook group.
The customers were also compared with the 20 neighbors who were especially efficient in saving energy.
The units came in various designs from local manufacturers; most were neither sturdy nor especially efficient.
They're especially efficient if you're going somewhere hot, and you're guaranteed wall-to-wall sunshine.
Muscle cells are especially efficient in absorbing carbohydrates from the blood just after exercise.
Collins was especially efficient on third down, going 3 for 4 for 49 yards.
Zinc sulfide and cadmium sulfide phosphors are especially efficient in electroluminescence.
The Eagles ran for 144 yards, often in short, relentless bursts, and were especially efficient on third down.
The Energy Star program, which identifies especially efficient products, evaluates many pieces of computer equipment, but not servers.
Second, microwaves in the 1 gigahertz to 10 gigahertz band appear to be especially efficient at generating excessive current within modern semiconductors.
It's an especially efficient form of vampirism, one with its own official beer and a mascot that invariably ends up looking like some sort of obliterated genital.
