Grating-based dark-field interferometry can be realized with lab-based, low-brilliance X-ray sources and provides scattering information of sample structures below the detector pixel size. This unique property allows promising medical imaging applications, especially for lung diseases. Structural damage in lung tissue caused by pulmonary emphysema or pulmonary carcinoma could be observed in radiographs by changes in the dark-field signal with high sensitivity at early stages, in contrast to the conventional absorption signal. Currently, the standard for diagnosis in the clinical routine of pulmonary diseases is absorption computed tomography (CT). The assessment of a larger number of samples with in vivo dark-field CT is limited by the rather long scan times, the order of 2 h, that are required to obtain sufficient CT data quality. In this work, a prototype in vivo, small-animal, dark-field CT is optimized with respect to CT measurements with the following: usage of an iterative reconstruction algorithm for the reduction of undersampling artifacts, a rearranged data acquisition scheme with reduced amount of dead time, and thinned gratings and curved grating geometry for more efficient utilization of the 37 kV X-ray flux. The device performance is evaluated with noise-effective dose measurements, image contrast-to-noise ratio, interferometry visibility across the field-of-view, and a reduced measurement time of 40 min with a deposited dose of 85 mGy.