PURPOSE: To optimize diffusion-relaxation MRI with tensor-valued diffusion encoding for precise estimation of compartment-specific fractions, diffusivities, and T values within a two-compartment model of white matter, and to explore the approach in vivo. METHODS: Sampling protocols featuring different b-values (b), b-tensor shapes (b ), and echo times (TE) were optimized using Cram\ er-Rao lower bounds (CRLB). Whole-brain data were acquired in children, adults, and elderly with white matter lesions. Compartment fractions, diffusivities, and T values were estimated in a model featuring two microstructural compartments represented by a "stick" and a "zeppelin." RESULTS: Precise parameter estimates were enabled by sampling protocols featuring seven or more "shells" with unique b/b /TE-combinations. Acquisition times were approximately 15 minutes. In white matter of adults, the "stick" compartment had a fraction of approximately 0.5 and, compared with the "zeppelin" compartment, featured lower isotropic diffusivities (0.6 vs. 1.3 μm /ms) but higher T values (85 vs. 65 ms). Children featured lower "stick" fractions (0.4). White matter lesions exhibited high "zeppelin" isotropic diffusivities (1.7 μm /ms) and T values (150 ms). CONCLUSIONS: Diffusion-relaxation MRI with tensor-valued diffusion encoding expands the set of microstructure parameters that can be precisely estimated and therefore increases their specificity to biological quantities.