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 and could indicate whether the interaction is predominantly spin-independent or spin-dependent. Our findings illustrate the importance of a low threshold in modulation searches.