  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.
