Spherical deconvolution methods have been applied to diffusion MRI to improve diffusion tensor tractography results in brain regions with multiple fibre crossing. Recent developments, such as the introduction of non-negative constraints on the solution, allow a more accurate estimation of fibre orientations by reducing instability effects due to noise robustness. Standard convolution methods do not, however, adequately model the effects of partial volume from isotropic tissue, such as gray matter, or cerebrospinal fluid, which may degrade spherical deconvolution results. Here we use a newly developed spherical deconvolution algorithm based on an adaptive regularization (damped version of the Richardson-Lucy algorithm) to reduce isotropic partial volume effects. Results from both simulated and in vivo datasets show that, compared to a standard non-negative constrained algorithm, the damped Richardson-Lucy algorithm reduces spurious fibre orientations and preserves angular resolution of the main fibre orientations. These findings suggest that, in some brain regions, non-negative constraints alone may not be sufficient to reduce spurious fibre orientations. Considering both the speed of processing and the scan time required, this new method has the potential for better characterizing white matter anatomy and the integrity of pathological tissue.