  We study the spin-independent neutralino Dark Matter scattering off heavy
nuclei in the MSSM. We identify analytically the blind spots in direct
detection for intermediate values of $m_A$. In the region where $\mu$ and
$M_{1,2}$ have opposite signs, there is not only a reduction of the lightest
CP-even Higgs coupling to neutralinos, but also a destructive interference
between the neutralino scattering through the exchange of the lightest CP-even
Higgs and that through the exchange of the heaviest CP-even Higgs. At critical
values of $m_A$, the tree-level contribution from the light Higgs exchange
cancels the contribution from the heavy Higgs, so the scattering cross section
vanishes. We denote these configurations as blind spots, since they provide a
generalization of the ones previously discussed in the literature, which occur
at very large values of $m_A$. We show that the generalized blind spots may
occur in regions of parameter space that are consistent with the obtention of
the proper neutralino relic density, and can be tested by non-standard Higgs
boson searches and EWino searches at the LHC and future linear colliders.
