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.
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