Integrating the underlying brain circuit's structural and functional architecture is required to explore the functional organization of cognitive networks. In that regard, we recently introduced the Functionnectome. This structural-functional method combines an fMRI acquisition with tractography-derived white matter connectivity data to map cognitive processes onto the white matter. However, this multimodal integration faces three significant challenges: (1) the necessarily limited overlap between tractography streamlines and the grey matter, which may reduce the amount of functional signal associated with the related structural connectivity; (2) the scrambling effect of crossing fibers on functional signal, as a single voxel in such regions can be structurally connected to several cognitive networks with heterogeneous functional signals; and (3) the difficulty of interpretation of the resulting cognitive maps, as crossing and overlapping white matter tracts can obscure the organization of the studied network. In the present study, we tackled these problems by developing a streamline-extension procedure and dividing the white matter anatomical priors between association, commissural, and projection fibers. This approach significantly improved the characterization of the white matter involvement in the studied cognitive processes. The new Functionnectome priors produced are now readily available, and the analysis workflow highlighted here should also be generalizable to other structural-functional approaches.