The invention relates to a radiation detector (100), particularly for X-rays (X) and for γ-rays, which comprises a combination of (a) at least one primary conversion layer (101a-101f) with a low attenuation coefficient for the photons and (b) at least one secondary conversion layer (102) with a high attenuation coefficient for the photons. In preferred embodiments, the primary conversion layer (101a-101f) may be realized by a silicon layer coupled to associated energy-resolving counting electronics (111a-111f, 121). The secondary conversion layer (102) may be realized for example by CZT or GOS coupled to energy-resolving counting electronics or integrating electronics. Using primary conversion layers with low stopping power allows to build a stacked radiation detector (100) for spectral CT in which the counting rates of the layers are limited to feasible values without requiring unrealistic thin layers.