Do current WIMP direct measurements constrain light relic neutralinos?

New upper bounds on direct detection rates have been presented recently by a number of experimental collaborations working on searches for weakly interacting massive particles (WIMPs). In this paper we analyze how the constraints on relic neutralinos which can be derived from these results are affected by the uncertainties in the distribution function of WIMPs in the halo. Various different categories of velocity distribution functions are considered, and the ensuing implications for supersymmetric configurations derived. We conservatively conclude that current experimental data do not constrain neutralinos of small mass (below 50 GeV).