  We show that the main features of the annual modulation of the signal
expected in a WIMP direct detection experiment, i.e. its sinusoidal dependence
with time, the occurrence of its maxima and minima during the year and (under
some circumstances) even the one-year period, may be affected by relaxing the
isothermal sphere hypothesis in the description of the WIMP velocity phase
space. The most relevant effect is a distortion of the time-behaviour at low
recoil energies for anisotropic galactic halos. While some of these effects
turn out to be relevant at recoil energies below the current detector
thresholds, some others could already be measurable, although some degree of
tuning between the WIMP mass and the experimental parameters would be required.
Either the observation or non-observation of these effects could provide clues
on the phase space distribution of our galactic halo.
