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. The upgrade includes a new detector support structure capable of accommodating 33 modules, the associated multichannel readout with 66 SQUID channels, a neutron shield, a calibration source lift, and the installation of a muon veto. 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 . The large crystal gives an accurate total energy measurement. The light detector permits a determination of the light yield for an event, allowing an effective separation of nuclear recoils from electron–photon backgrounds. Furthermore, 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 ∼10 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 × 10 - 7 pb , at M WIMP ∼ 50 GeV .