  We consider the alignment torque between a spinning black hole and an
accretion disc whose angular momenta are misaligned. This situation must hold
initially in almost all gas accretion events on to supermassive black holes,
and may occur in binaries where the black hole receives a natal supernova kick.
We show that the torque always acts to align the hole's spin with the total
angular momentum without changing its magnitude. The torque acts dissipatively
on the disc, reducing its angular momentum, and aligning it with the hole if
and only if the angle theta between the angular momenta J_d of the disc and J_h
of the hole satisfies the inequality cos theta > -J_d / 2 J_h. If this
condition fails, which requires both theta > pi/2 and J_d < 2 J_h, the disc
counteraligns.
