We present a new application of a focusing regularization scheme for the inversion of resistivity and induced polarization (IP) data that supports large resistivity magnitude and phase contrasts. Similar approaches so far have only been used for the interpretation of gravity, magnetic, or seismic data sets. Unlike methods based on smoothness constraints, the approach is able to resolve sharp boundaries of bodies and layers, and it allows slight parameter variations within them. Therefore, it can be used in hydrogeologic applications where we need focused images to resolve high-contrast aquifer boundaries. Our approach is based on the minimum gradient support, which seeks to minimize the occurrence of parameter contrasts, independent of their magnitude. We study the effects of a variable control parameter on the reweighting optimization, allowing a continuous transition from smooth to sharp images. We also take the spatially varying sensitivity into account to allow focusing even where sensitivities are small. The implemented weighting leads to increased smoothing in well-resolved areas and a decrease in regions of lower sensitivity. The opposite approach is examined as well. This gradient-dependent sensitivity weighting is basically an extension of depth-dependent sensitivity weighting. We demonstrate the effectiveness and limitations of the approach and the influence of the control parameter using different synthetic models and field data from a hydrogeophysical test site. The technique has proven particularly suitable for revealing sharp parameter contrasts.