Diffusion MRI measures micron scale displacement of water molecules, providing unique insight into microstructural tissue architecture. However, current practical image resolution is in the millimeter scale, and thus diffusivities from many tissue compartments are averaged in each voxel, reducing the sensitivity and specificity of the measurement to subtle pathologies. Recent studies have pointed out that eliminating the contribution of extracellular water increases the sensitivity of the diffusion measures to tissue architecture. Moreover, in brain imaging, estimation of the extracellular volume appears to indicate pathological processes such as atrophy, edema and neuroinflammation. Here we study the free-water method, which assumes a bi-tensor model. We add low b-value shells to a regular DTI acquisition and present methods to improve the estimation of the model parameters using the extra information. In addition, we define a Laplace-Beltrami regularization operator that further stabilizes the multi-shell estimation.