Regularized regression is a standard method for obtaining the DRT, but it is characterized by several shortcomings, such as the selection of a distance. Our work demonstrates that directly regressing impedance data against the DRT model, employing the 1-distance for the data/model discrepancy and the 1-norm for the penalty, generally yields higher accuracy than conventional RR and other studied pairs comprising 1 and infinity norms. This advantage is particularly pronounced for discontinuous DRTs and datasets containing outliers. This novel approach offers