We introduce a comprehensive method for space-borne 3-D volumetric scattering-tomography of cloud microphysics, developed for the CloudCT mission. The retrieved microphysical properties are the liquid-water-content (LWC) and effective droplet radius within a cloud. We include a model for a perspective polarization imager and an assumption of 3-D variation of the effective radius. Elements of our work include computed tomography initialization by a parametric horizontally uniform microphysical model. This results in smaller errors than the prior art. The mean absolute errors of the retrieved LWC and effective radius are reduced from 62% and 28% to 40% and 9%, respectively. The parameters of this initialization are determined by a grid search of a cost function. Furthermore, we add viewpoints in the cloudbow region, to better sample the polarized scattering phase function. The suggested advances are evaluated by retrieval of a set of clouds generated by large-eddy simulations.