Microstructure imaging aims to estimate specific quantities such as the axonal density through modeling of diffusion MRI (dMRI) data. However, the low information content of conventional dMRI necessitates assumptions limiting the estimates’ accuracy. Here, we show how to replace model assumptions with independent information from tensor-valued diffusion encoding and diffusion-relaxation experiments. We present sampling protocols optimized using Cramér-Rao lower bounds allowing precise whole-brain estimation of compartment-specific fractions, diffusivities and T2 values in 15 minutes and show results from subjects of different ages. The approach greatly expands the set of parameters measurable with dMRI and provides parameter relations informing model constraints.