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Relating brain tissue properties to diffusion tensor imaging (DTI) is limited when an image voxel contains partial volume of brain tissue with free water, such as cerebrospinal fluid or edema, rendering the DTI indices no longer useful for describing the underlying tissue properties. We propose here a method for separating diffusion properties of brain tissue from surrounding free water while mapping the free water volume. This is achieved by fitting a bi-tensor model for which a mathematical framework is introduced to stabilize the fitting. Applying the method on datasets from a healthy subject and a patient with edema yielded corrected DTI indices and a more complete tract reconstruction that passed next to the ventricles and through the edema. We were able to segment the edema into areas according to the condition of the underlying tissue. In addition, the volume of free water is suggested as a new quantitative contrast of diffusion MRI. The findings suggest that free water is not limited to the borders of the brain parenchyma; it therefore contributes to the architecture surrounding neuronal bundles and may indicate specific anatomical processes. The analysis requires a conventional DTI acquisition and can be easily merged with existing DTI pipelines.