A stable, accurate and robust-to-noise method for the estimation of the intra-voxel bundle-wise diffusion properties for diffusion-weighted magnetic resonance imaging is presented. The proposed method overcomes some of the limitations of most of the multi-fiber algorithms in the literature and extends them to estimate the diffusion profiles, improving the estimation of the intra-voxel geometry at challenging microstructure configurations, that is to say: relatively small crossing angles, different voxel-wise anisotropic diffusion profiles and low SNR. The proposed methodology is based on four key novel ideas: (i) A Multi-Resolution Discrete-Search determines the orientation of the fiber bundles accurately and naturally constrains the sparsity on the recovered solutions; (ii) the determination of the number of fiber bundles using the F-test combined with a Rician bias correction; (iii) a Simultaneous Denoising and Fitting procedure that exploits the spatial redundancy of the axon bundles to achieve robustness with respect to noise; and (iv) a general framework for the estimation of the axial and radial diffusivity parameters independently for each voxel. A new useful evaluation metric is also proposed, which combines the information of the success rate in the estimated number of bundles and the angular error, avoiding in this way, some of the limitations these metrics have individually. A novel methodology for the evaluation of the methods on in-vivo data is also proposed. This work presents an extensive evaluation: the proposed methodology has been tested on state-of-the-art biophysical synthetic data for a variety of conditions, on the challenging spatially coherent phantom used on the HARDI reconstruction Challenge 2012, and on the recently released in-vivo MASSIVE data-set. Our results present significant improvements on the estimation of the number and orientation of the fiber bundles over the Spherical Deconvolution algorithm for multi-shell data, which is one of the most widely used multi-fiber algorithm. The results also show that, by the voxel-wise estimation of the diffusion profiles, the axial and radial diffusivity parameters are robustly estimated, being this essential for a better understanding of the individual bundle diffusion properties at challenging structural configurations.