Combination of diffusion weighted MRI with orthogonal measures such as T2- or T2*-weighting has been proposed to overcome the fit degeneracy found in microstructure modeling of diffusion signals. However, the repetition of diffusion measurements at different TE leads to unacceptably long acquisition times, hindering clinical applicability of this approach. Here, we propose accelerated acquisitions using diffusion weighted multi-spin and multi-gradient echo trains which sample the signal at several TEs after a standard diffusion encoding spin echo. In the current configurations these sequences speed up the acquisitions by 2.6x or 3.6x respectively. We validate these approaches on a phantom.