  An annual modulation in the event rate of the NaI detector of the DAMA
collaboration has been used to infer the existence of particle dark matter in
the Galactic halo. Bounds on the WIMP mass and WIMP-nucleon cross section have
been derived. These analyses have assumed that the local dark-matter velocity
distribution is either isotropic or has some bulk rotation. Here we consider
the effects of possible structure in the WIMP velocity distribution on the
annual-modulation amplitude. We show that if we allow for a locally anisotropic
velocity dispersion tensor, the interpretation of direct detection experiments
could be altered significantly. We also show that uncertainties in the velocity
distribution that arise from uncertainties in the radial density profile are
less important if the velocity dispersion is assumed to be isotropic.
