  A weakly interacting massive particle (WIMP) weighing only a few GeV has been
invoked as an explanation for the signal from the DAMA/LIBRA experiment. We
show that the data from DAMA/LIBRA are now powerful enough to strongly
constrain the properties of any putative WIMP. Accounting for the detailed
recoil spectrum, a light WIMP with a Maxwellian velocity distribution and a
spin-independent (SI) interaction cannot account for the data. Even neglecting
the spectrum, much of the parameter space is excluded by limits from the DAMA
unmodulated signal at low energies. Significant modifications to the
astrophysics or particle physics can open light mass windows.
