  The DAMA experiment searches for Weakly Interacting Massive Particle (WIMP)
dark matter via its expected but rare interactions within the detector, where
the interaction rates will modulate throughout the year due to the orbital
motion of the Earth. Over the course of more than 10 years of operation, DAMA
has indeed detected a strong modulation in the event rate above the detector
threshold of 2 keVee. Under standard assumptions regarding the dark matter halo
and WIMP interactions, this signal is consistent with that expected of WIMPs of
two different approximate masses: ~ 10 GeV and ~ 70 GeV. We examine how a lower
threshold, allowed by recent upgrades to the DAMA detector, may shed light on
this situation. We find that the lower threshold data should rule out one of
the two mass ranges for spin-independent couplings (in the worst case,
disfavoring one of the masses by still more than 2.6$\sigma$) and is likely,
though not certain, to do the same for spin-dependent couplings. Furthermore,
the data may indicate whether the interaction is predominantly spin-independent
or spin-dependent in some cases. Our findings illustrate the importance of a
low threshold in modulation searches.
