  The common analysis of direct searches for spin-independent Weakly
Interacting Massive Particles (WIMPs) assumes that a spin-independent WIMP
couples with the same strength with both nucleons, \textit{i.e.} that the
spin-independent interaction is also fully isospin-independent. Though in a
fully isospin-dependent interaction scenario the spin-independent WIMP-nucleus
cross section is strongly quenched, the leading experiments are still sensitive
enough to set limits 1-2 orders of magnitude less stringent than those
traditionally presented. In the isospin-dependent scenario the difference
between the limits of CDMS-II and ZEPLIN-I is significantly reduced. Here, a
model-independent framework is discussed and applied to obtain the current
general model-independent limits.

High Energy Physics - Phenomenology;Astrophysics