One-dimensional (1D) velocity models are still widely used for computing earthquake locations at seismological centers or in regions where three-dimensional (3D) velocity models are not available due to the lack of data of sufficiently high quality. The concept of the minimum 1D model with appropriate station corrections provides a framework to compute initial hypocenter locations and seismic velocities for local earthquake tomography. Since a minimum 1D model represents a solution to the coupled hypocenter-velocity problem it also represents a suitable velocity model for earthquake location and data quality assessment, such as evaluating the consistency in assigning pre-defined weighting classes and average picking error. Nevertheless, the use of a simple 1D velocity structure in combination with station delays raises the question of how appropriate the minimum 1D model concept is when applied to complex tectonic regions with significant three-dimensional (3D) variations in seismic velocities. In this study we compute one regional minimum 1D model and three local minimum 1D models for selected subregions of the Swiss Alpine region, which exhibits a strongly varying Moho topography. We compare the regional and local minimum 1D models in terms of earthquake locations and data quality assessment to measure their performance. Our results show that the local minimum 1D models provide more realistic hypocenter locations and better data fits than a single model for the Alpine region. We attribute this to the fact that in a local minimum 1D model local and regional effects of the velocity structure can be better separated. Consequently, in tectonically complex regions, minimum 1D models should be computed in sub-regions defined by similar structure, if they are used for earthquake location and data quality assessment.