Purpose: To enable a preliminary assessment of the suitability of edge illumination (EI) x-ray phase contrast (XPC) micro x-ray computed tomography (micro-CT) to preclinical imaging. Specifically, to understand how different acquisition schemes and their combination with dedicated data processing affect contrast-to-noise ratio (CNR) and spatial resolution, while providing control over scan time and radiation dose delivery. Procedures: Deceased mice (n = 3) were scanned with an EI XPC micro-CT setup operated under different settings, leading to scan times between 18 h and 13 min. For the shortest scan, the entrance dose was measured with a calibrated PTW 23344 ion chamber. Different data processing methods were applied, retrieving either separate attenuation and phase images, or hybrid (combined attenuation and phase) images. A quantitative comparison was performed based on CNR and spatial resolution measurements for a soft tissue interface. Results: All phase-based images have led to a higher CNR for the considered soft tissue interface than the attenuation image, independent of scan time. The best relative CNR (a sixfold increase) was observed in one of the hybrid images. Spatial resolution was found to be connected to scan time, with a resolution of approximately 20 μm and 60 μm achieved for the longest and shortest scans, respectively. An entrance dose of approximately 300 mGy was estimated for the scan performed within 13 min. Conclusions: Despite their preliminary nature, our results suggest that EI XPC bears potential for enhancing the utility of preclinical micro-CT, and, pending further research and development, could ultimately become a valuable technique in this field.