The CRESST cryogenic direct dark matter search at Gran Sasso, searching for WIMPs via nuclear recoil, has been upgraded to CRESST-II by several changes and improvements.We present the results of a commissioning run carried out in 2007. The basic element of CRESST-II is a detector module consisting of a large (~ 300 g) CaWO_4 crystal and a very sensitive smaller (~ 2 g) light detector to detect the scintillation light from the CaWO_4.Information from light-quenching factor studies allows the definition of a region of the energy-light yield plane which corresponds to tungsten recoils. A neutron test is reported which supports the principle of using the light yield to identify the recoiling nucleus. Data obtained with two detector modules for a total exposure of 48 kg-days are presented. Judging by the rate of events in the all nuclear recoils acceptance region the apparatus shows a factor ~ten improvement with respect to previous results, which we attribute principally to the presence of the neutron shield. In the tungsten recoils acceptance region three events are found, corresponding to a rate of 0.063 per kg-day. Standard assumptions on the dark matter flux, coherent or spin independent interactions,then yield a limit for WIMP-nucleon scattering of 4.8 times 10^{-7}pb, at M{WIMP} ~50 GeV.
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