A method and a dual-source CT are disclosed. In at least one embodiment, the projection data of the integrating and of the counting detector from a quarter rotation of the gantry is used jointly for reconstruction of a first tomographic image dataset, the energy-resolved projection data of the counting detector from at least one half rotation of the gantry being used for reconstruction of at least a second material-selective tomographic image dataset, and at least one tomographic result image dataset being formed by overlaying the first tomographic image dataset with the material selection of the second image dataset.