  The comparison of the results of direct detection of Dark Matter, obtained
with various target nuclei, requires model-dependent, or even arbitrary,
assumptions. Indeed, to draw conclusions either the spin-dependent (SD) or the
spin-independent (SI) interaction has to be neglected. In the light of the null
results from supersymmetry searches at the LHC, the squark sector is pushed to
high masses. We show that for a squark sector at the TeV scale, the framework
used to extract contraints from direct detection searches can be redefined as
the number of free parameters is reduced. Moreover, the correlation observed
between SI and SD proton cross sections constitutes a key issue for the
development of the next generation of Dark Matter detectors.
