  The inelastic dark matter scenario was proposed to reconcile the DAMA annual
modulation with null results from other experiments. In this scenario, WIMPs
scatter into an excited state, split from the ground state by an energy delta
comparable to the available kinetic energy of a Galactic WIMP. We note that for
large splittings delta, the dominant scattering at DAMA can occur off of
thallium nuclei, with A~205, which are present as a dopant at the 10^-3 level
in NaI(Tl) crystals. For a WIMP mass m~100GeV and delta~200keV, we find a
region in delta-m-parameter space which is consistent with all experiments.
These parameters in particular can be probed in experiments with thallium in
their targets, such as KIMS, but are inaccessible to lighter target
experiments. Depending on the tail of the WIMP velocity distribution, a highly
modulated signal may or may not appear at CRESST-II.
