Phase sensitive x-ray imaging expands the applicability of standard attenuation based techniques by offering several orders of magnitude of increase in sensitivity. Due to the short wavelength, x-ray phase is not directly measurable, but has to be put in evidence by the use of phase contrast techniques. The phase can then be reconstructed from one or several phase contrast images. In this study, we consider synchrotron x-ray phase micro-computed tomography (μCT) based on free space propagation for heterogeneous and strongly absorbing objects. This technique generally relies on acquiring several scans of the sample at different detector distances. It is also generally believed that multi-distance phase μCT needs a higher dose input than single distance phase μCT. The purpose of this work is to study the impact of different means of dose fractionation on the reconstructed image quality. We define different acquistion schemes in multi-distance in-line phase μCT. Previously, the exposure time at each sample-to-detector distance was usually kept the same. Here, we let not only the number of distances vary but also the fraction of exposure time at each distance, the total exposure time being kept constant. Phase retrieval is performed with the mixed approach algorithm. The reconstructed μCT images are compared in terms of accuracy, precision and resolution. In addition, we also compare the result of dose fractionated multi distance phase μCT to single distance phase μCT using the same total radiation dose. In the multi-distance approach, we find that using different exposure times on each distance improves the image quality in the reconstructed image. Further, we show that, despite having the same total dose delivery, the multi distance imaging method gives better image quality than the single distance method, at the cost of an additional overhead from camera displacements and reference images. We show that by optimizing the acquistion parameters in terms of number of distances and exposure time at each distance, the resulting image quality can be improved. This means that for a desired image quality, a lower radiation dose can be used. This is important especially in high resolution imaging where the radiation dose used for imaging can be very large, potentially damaging the sample. Based on the acquired data, we define an optimal protocol for use in together with the heterogeneous object mixed approach.