  We reinvestigate the effect of annihilations on the distribution of
collisionless dark matter (DM) in a spherical density spike around a massive
black hole. We first construct a very simple, pedagogic, analytic model for an
isotropic phase space distribution function that accounts for annihilation and
reproduces the "weak cusp" found by Vasiliev for DM deep within the spike and
away from its boundaries. The DM density in the cusp varies as $r^{-1/2}$ for
$s$-wave annihilation, where $r$ is the distance from the central black hole,
and is not a flat "plateau" profile. We then extend this model by incorporating
a loss cone that accounts for the capture of DM particles by the hole. The loss
cone is implemented by a boundary condition that removes capture orbits,
resulting in an anisotropic distribution function. Finally, we evolve an
initial spike distribution function by integrating the Boltzmann equation to
show how the weak cusp grows and its density decreases with time. We treat two
cases, one for $s$-wave and the other for $p$-wave DM annihilation, adopting
parameters characteristic of the Milky Way nuclear core and typical WIMP models
for DM. The cusp density profile for $p$-wave annihilation is weaker, varying
like $\sim r^{-0.34}$, but is still not a flat plateau.
