The feasibility of computed tomography (CT) with energy-resolved x-ray detection has been investigated. A breast CT design with multi slit multi slice (MSMS) data acquisition was used for this study. The MSMS CT includes linear arrays of photon counting detectors separated by gaps. This CT configuration allows for efficient scatter rejection and 3D data acquisition. The energy-resolved CT images were simulated using a digital breast phantom and the design parameters of the proposed MSMS CT. The phantom had 14 cm diameter and 50/50 adipose/glandular composition, and included carcinoma, adipose, blood, iodine and CaCO3 as contrast elements. The x-ray technique was 90 kVp tube voltage with 660 mR skin exposure. Photon counting, charge (energy) integrating and photon energy weighting CT images were generated. The contrast-to-noise (CNR) improvement with photon energy weighting was quantified. The dual energy subtracted images of CaCO3 and iodine were generated using a single CT scan at a fixed x-ray tube voltage. The x-ray spectrum was electronically split into low- and high-energy parts by a photon counting detector. The CNR of the energy weighting CT images of carcinoma, blood, adipose, iodine, and CaCO3 was higher by a factor of 1.16, 1.20, 1.21, 1.36 and 1.35, respectively, as compared to CT with a conventional charge (energy) integrating detector. Photon energy weighting was applied to CT projections prior to dual energy subtraction and reconstruction. Photon energy weighting improved the CNR in dual energy subtracted CT images of CaCO3 and iodine by a factor of 1.35 and 1.33, respectively. The combination of CNR improvements due to scatter rejection and energy weighting was in the range of 1.71–2 depending on the type of the contrast element. The tilted angle CZT detector was considered as the detector of choice. Experiments were performed to test the effect of the tilting angle on the energy spectrum. Using the CZT detector with 20° tilting angle decreased the tailing of the measured x-ray spectrum as compared to a conventional CZT detector. It was concluded that the energy-resolved MSMS CT with tilted angle CZT detector is potentially feasible and could provide a unique combination of photon counting, energy weighting, scatter rejection and single kVp dual energy subtraction CT imaging.