The CRESST experiment aims for a detection of dark matter in the form of WIMPs. These particles are expected to scatter elastically off the nuclei of a target material, thereby depositing energy on the recoiling nucleus. CRESST uses scintillating CaWO4 crystals as such a target. The energy deposited by an interacting particle is primarily converted to phonons which are detected by transition edge sensors. In addition, a small fraction of the interaction energy is emitted from the crystals in the form of scintillation light which is measured in coincidence with the phonon signal by a separate cryogenic light detector for each target crystal. The ratio of light to phonon energy permits the discrimination between the nuclear recoils expected from WIMPs and events from radioactive backgrounds which primarily lead to electron recoils. CRESST has shown the success of this method in a commissioning run in 2007 and, since then, further investigated possibilities for an even better suppression of backgrounds. Here, we report on a new class of background events observed in the course of this work. The consequences of this observation are discussed and we present the current status of the experiment.