  We investigate a new type of dark matter with couplings to ordinary matter
naturally suppressed by at least one order of magnitude compared to weak
interactions. Despite the extra-weak interactions massive particles of this
type (XWIMPs) can satisfy the WMAP relic density constraints due to
coannihilation if their masses are close to that of the lightest state of the
MSSM. The region in the parameter space of a suitably extended mSUGRA model
consistent with the WMAP3 constraints on XWIMPs is determined. Plots for
sparticles masses are given which can be subject to test at the LHC. We also
discuss the sensitivity of the analysis to the top mass. As an example for an
explicit model we show that such a form of dark matter can arise in certain
$Z'$ extensions of the MSSM. Specifically we consider an abelian extension with
spontaneous gauge symmetry breaking via Fayet-Iliopoulos D-terms in the hidden
sector. The LSP of the full model arises from the extra $U(1)_X$ sector with
extra-weak couplings to Standard Model particles due to experimental
constraints. With R-parity conservation the new XWIMP is a candidate for cold
dark matter. In a certain limit the model reduces to the \st extension of the
MSSM without a Higgs mechanism, and wider ranges of models with similar
characteristics are easy to construct.
