  Gravitational-wave signals from black-hole binaries with non-precessing spins
are described by four parameters -- each black hole's mass and spin. It has
been shown that the dominant spin effects can be modeled by a \emph{single}
spin parameter, leading to the development of several \emph{three-parameter}
waveform models. Previous studies indicate that these models should be adequate
for gravitational-wave detection. In this paper we focus on the systematic
biases that would result from using them to estimate binary parameters, and
consider a one-parameter family of configurations at one choice of mass ratio
and effective single spin. We find that for low-mass binaries within that
family of configurations, where the observable waveform is dominated by the
inspiral, the systematic bias in all physical parameters is smaller than the
parameter uncertainty due to degeneracies between the mass ratio and the spins,
at least up to signal-to-noise ratios (SNRs) of 50. For higher-mass binaries,
where the merger and ringdown make a greater contribution to the observed
signal, the bias in the mass ratio is comparable to its uncertainty at SNRs of
only $\sim$30, and the bias in the measurement of the total spin is
\emph{larger} than the uncertainty defined by the 90% confidence region even at
an SNR of only 10. Although this bias may be mitigated in future models by a
better choice of single-effective-spin parameter, these results suggest that it
may be possible to accurately measure \emph{both} black-hole spins in
intermediate-mass binaries.
