This paper presents MicroTrack, an algorithm that combines global tractography and direct microstructure estimation using diffusion-weighted imaging data. Previous work recovers connectivity via tractography independently from estimating microstructure features, such as axon diameter distribution and density. However, the two estimates have great potential to inform one another given the common assumption that microstructural features remain consistent along fibers. Here we provide a preliminary examination of this hypothesis. We adapt a global tractography algorithm to associate axon diameter with each putative pathway and optimize both the set of pathways and their microstructural parameters to find the best fit of this holistic white-matter model to the MRI data. We demonstrate in simulation that, with a multi-shell HARDI acquisition, this approach not only improves estimates of microstructural parameters over voxel-by-voxel estimation, but provides a solution to long standing problems in tractography. In particular, a simple experiment demonstrates the resolution of the well known ambiguity between crossing and kissing fibers. The results strongly motivate further development of this kind of algorithm for brain connectivity mapping.