Diffusion MRI streamlines tractography suffers from a number of inherent limitations, one of which is the accurate determination of when streamlines should be terminated. Use of an accurate streamlines propagation mask from segmentation of an anatomical image confines the streamlines to the volume of the brain white matter, but does not take full advantage of all of the information available from such an image. We present a modular addition to streamlines tractography, which makes more effective use of the information available from anatomical image segmentation, and the known properties of the neuronal axons being reconstructed, to apply biologically realistic priors to the streamlines generated; we refer to this as "Anatomically-Constrained Tractography". Results indicate that some of the known false positives associated with tractography algorithms are prevented, such that the biological accuracy of the reconstructions should be improved, provided that state-of-the-art streamlines tractography methods are used.