Diffusion tensor imaging (DTI) has been extensively used to map changes in brain tissue related to neurological disorders. Among the most widespread DTI findings are increased mean diffusivity and decreased fractional anisotropy of white matter tissue in neurodegenerative diseases. Here we utilize multi-shell diffusion imaging to separate diffusion signal of the brain parenchyma from non-parenchymal fluid within the white matter. We show that unincorporated anisotropic water in perivascular space (PVS) significantly, and systematically, biases DTI measures, casting new light on the biological validity of many previously reported findings. Despite the challenge this poses for interpreting these past findings, our results suggest that multi-shell diffusion MRI provides a new opportunity for incorporating the PVS contribution, ultimately strengthening the clinical and scientific value of diffusion MRI.