We show that each integral block of parabolic category O (including singular
ones) for a semi-simple Lie group can be realized as a full subcategory of a
``thick'' category O over a finite W-algebra for the same Lie group.

The nilpotent used to construct this finite W-algebra is determined by the
central character of the block, and the subcategory taken is that killed by a
two-sided ideal depending on the original parabolic. The equivalences in
question are induced by those of Milicic-Soergel and Skryabin.

We also give a proof of a result of some independent interest: the singular
blocks of parabolic category O can be geometrically realized as ``partial
Whittaker sheaves'' on partial flag varieties.