  Detection template families (DTFs) are built to capture the essential
features of true gravitational waveforms using a small set of phenomenological
waveform parameters. Buonanno, Chen, and Vallisneri [Phys. Rev. D 67, 104025
(2003)] proposed the ``BCV2'' DTF to perform computationally efficient searches
for signals from precessing binaries of compact stellar objects. Here we test
the signal-matching performance of the BCV2 DTF for asymmetric--mass-ratio
binaries, and specifically for double--black-hole binaries with component
masses (m1,m2): (6~12Msun, 1~3Msun), and for black-hole--neutron-star binaries
with component masses (m1,m2) = (10Msun, 1.4Msun); we take all black holes to
be maximally spinning. We find a satisfactory signal-matching performance, with
fitting factors averaging between 0.94 and 0.98. We also scope out the region
of BCV2 parameters needed for a template-based search, we evaluate the template
match metric, we discuss a template-placement strategy, and we estimate the
number of templates needed for searches at the LIGO design sensitivity. In
addition, after gaining more insight in the dynamics of spin--orbit precession,
we propose a modification of the BCV2 DTF that is parametrized by physical
(rather than phenomenological) parameters. We test this modified ``BCV2P'' DTF
for the (10Msun, 1.4Msun) black-hole--neutron-star system, finding a
signal-matching performance comparable to the BCV2 DTF, and a reliable
parameter-estimation capability for target-binary quantities such as the chirp
mass and the opening angle (the angle between the black-hole spin and the
orbital angular momentum).
