Energy-dispersive X-ray spectroscopy (EDS) tomography is an advanced technique to characterize compositional information for nanostructures in three dimensions (3D). However, the application is hindered by the poor image quality caused by the low signal-to-noise ratios and the limited number of tilts, which are fundamentally limited by the insufficient number of X-ray counts. In this paper, we explore how to make accurate EDS reconstructions from such data. We propose to augment EDS tomography by joining with it a more accurate high-angle annular dark-field STEM (HAADF-STEM) tomographic reconstruction, for which usually a larger number of tilt images are feasible. This augmentation is realized through total nuclear variation (TNV) regularization, which encourages the joint EDS and HAADF reconstructions to have not only sparse gradients but also common edges and parallel (or antiparallel) gradients. Our experiments show that reconstruction images are more accurate compared to the non-regularized and the total variation regularized reconstructions, even when the number of tilts is small or the X-ray counts are low.