We present a new focal mechanism stress inversion technique to produce regional-scale models of stress orientation containing the minimum complexity necessary to fit the data. Current practice is to divide a region into small subareas and to independently fit a stress tensor to the focal mechanisms of each subarea. This procedure may lead to apparent spatial variability that is actually an artifact of overfitting noisy data or nonuniquely fitting data that does not completely constrain the stress tensor. To remove these artifacts while retaining any stress variations that are strongly required by the data, we devise a damped inversion method to simultaneously invert for stress in all subareas while minimizing the difference in stress between adjacent subareas. This method is conceptually similar to other geophysical inverse techniques that incorporate damping, such as seismic tomography. In checkerboard tests, the damped inversion removes the stress rotation artifacts exhibited by an undamped inversion, while resolving sharper true stress rotations than a simple smoothed model or a moving-window inversion. We show an example of a spatially damped stress field for southern California. The methodology can also be used to study temporal stress changes, and an example for the Coalinga, California, aftershock sequence is shown. We recommend use of the damped inversion technique for any study examining spatial or temporal variations in the stress field.