Direct solutions of the dipole inversion problem in quantitative susceptibility mapping (QSM) are computationally efficient but plagued by streaking artifacts. Here, we have shown that non-uniform sampling of frequency space can achieve additional streaking artifact reduction compared to QSM with thresholded k-space division and state-of-the-art regularisation. By avoiding sampling areas in frequency space where the solution is not well defined, the solution of the ill-posed inverse problem is made more robust and noise amplification is reduced. This approach could be combined with compressed sensing techniques to further improve the QSM reconstruction. This research uses open-source tools from the MR community.