  The SIMPLE project uses superheated C2ClF5 liquid detectors to search for
particle dark matter candidates. We report the results of the first stage
exposure (14.1 kgd) of its latest two-stage, Phase II run, with 15 superheated
droplet detectors of total active mass 0.208 kg. In combination with the
results of the neutron-spin sensitive XENON10 experiment, these results yield a
limit of |a_p| < 0.32, |a_n| < 0.17 for M_W = 50 GeV/c2 on the
model-independent, spin-dependent sector of weakly interacting massive particle
(WIMP)-nucleus interactions, and together yield a 50% reduction in the
previously allowed region of the phase space. The result provides a contour
minimum of {\sigma}_p ~ 2.8 x 10-2 pb at M_W = 45 GeV/c2, constituting the most
restrictive direct detection limit to date against a spin-dependent WIMP-proton
coupling. In the spin-independent sector, the result is seen to offer the
prospect of contributing to the question of light mass WIMPs with an
improvement in the current understanding of its nucleation efficiency.
