  We compute the capture rate for Dark Matter in the Sun for models where the
dominant interaction with nuclei is inelastic -- the Dark Matter up-scatters to
a nearby dark "partner" state with a small splitting of order a 100 keV. Such
models have previously been shown to be compatible with DAMA/LIBRA data, as
well as data from all other direct detection experiments. The kinematics of
inelastic Dark Matter ensures that the dominant contribution to capture occurs
from scattering off of iron. We give a prediction for neutrino rates for
current and future neutrino telescopes based on the results from current direct
detection experiments. Current bounds from Super--Kamiokande and IceCube-22
significantly constrain these models, assuming annihilations are into two-body
Standard Model final states, such as W+W-, t-tbar, b-bbar or tau+tau-.
Annihilations into first and second generation quarks and leptons are generally
allowed, as are annihilations into new force carriers which decay dominantly
into e+e-, mu+mu- and pi+pi-.
