  We prove that the derived categories of abelian categories have unique
enhancements -- all of them, the unbounded, bounded, bounded above and bounded
below derived categories. The unseparated and left completed derived categories
of a Grothendieck abelian category are also shown to have unique enhancements.
Finally we show that the derived category of complexes with quasi-coherent
cohomology and the category of perfect complexes have unique enhancements for
quasi-compact and quasi-separated schemes.
