  Gravitational wave searches to date have largely focused on non-precessing
systems. Including precession effects greatly increases the number of templates
to be searched over. This leads to a corresponding increase in the
computational cost and can increase the false alarm rate of a realistic search.
On the other hand, there might be astrophysical systems that are entirely
missed by non-precessing searches. In this paper we consider the problem of
constructing a template bank using stochastic methods for
neutron-star--black-hole binaries allowing for precession, but with the
restrictions that the orientation of the total angular momentum of the binary
is pointing towards the detector and that the neutron-star spin is negligible
relative to that of the black-hole. We quantify the number of templates
required for the search, and we explicitly construct the template bank. We show
that despite the large number of templates, stochastic methods can be adapted
to solve the problem. We quantify the parameter space region over which the
non-precessing search might miss signals.
