Abstract. Diffusion MRI is a frequently-used imaging modality that is used to infer microstructural properties of tissue, down to the scale of microns. For single-compartment models, such as the diffusion tensor, the interpretation of the models depends on the voxels having homogeneous tissue. This limitation makes it difficult to directly measure diffusion parameters for small structures such as the fornix, which may have partial volume in every voxel. In this work, we use a segmentation from a structural scan to calculate the tissue composition for each voxel in diffusion space. We model the signal from a voxel as a linear combination of the signals from these components, and thus fit parameters on a per-region basis. Fitting diffusion parameters to all regions, simultaneously, bolsters the data for small regions, which allows accurate estimation of the diffusion parameters. We test the proposed method by using diffusion data from the HCP. We downsample the HCP data, and show that our method returns parameter estimates that are closer to the high-resolution ground truths than region-of-interest methods. We apply our technique to the diffusion parameters in the fornix for adults born extremely preterm and matched controls. We show that our method estimates diffusion parameters accurately for structures that are small, compared to a typical diffusion MRI resolution.