  Relativistic spin-orbit and spin-spin couplings has been shown to modify the
gravitational waveforms expected from inspiraling binaries with a black hole
and a neutron star. As a result inspiral signals may be missed due to
significant losses in signal-to-noise ratio, if precession effects are ignored
in gravitational-wave searches. We examine the sensitivity of the anticipated
loss of signal-to-noise ratio on two factors: the accuracy of the precessing
waveforms adopted as the true signals and the expected distributions of
spin-orbit tilt angles, given the current understanding of their physical
origin. We find that the results obtained using signals generated by
approximate techniques are in good agreement with the ones obtained by
integrating the 2PN equations. This shows that a complete account of all
high-order post-Newtonian effects is usually not necessary for the
determination of detection efficiencies. Based on our current astrophysical
expectations, large tilt angles are not favored and as a result the decrease in
detection rate varies rather slowly with respect to the black hole spin
magnitude and is within 20--30% of the maximum possible values.
