  A large class of viable dark matter models contain a WIMP candidate that is a
component of a new electroweak multiplet whose mass $M$ is large compared to
the electroweak scale $m_W$. A generic amplitude-level cancellation in such
models yields a severe suppression of the cross section for WIMP-nucleon
scattering, making it important to assess the impact of formally subleading
effects. The power correction of order $m_W/M$ to the heavy WIMP limit is
computed for electroweak doublet (Higgsino-like) dark matter candidates, and a
modern model of nuclear modifications to the free nucleon cross section is
evaluated. Corrections to the pure Higgsino limit are determined by a single
parameter through first order in the heavy WIMP expansion. Current and
projected experimental bounds on this parameter are investigated. The direct
detection signal in the pure Higgsino limit remains below neutrino backgrounds
for WIMPs in the TeV mass range. Nuclear corrections are applied also to the
heavy Wino case, completing the investigation of combined subleading effects
from perturbative QCD, $1/M$ power corrections, and nuclear modifications.
