We propose an analytic technique for reducing sidelobe artifacts in synthetic aperture radar data. The technique, called leakage energy minimization (LEM), uses a spatially varying aperture function, the coefficients of which satisfy a simple optimality condition. The integrated sidelobe energy (or leakage energy) characterizing a given aperture weighting function is used as a metric for determining the likelihood of an aperture weighting. When applied to synthetic aperture radar data, the technique can effectively reduce sidelobe levels with negligible loss of resolution. The algorithm is computationally efficient, and its application requires no restrictions on the data sampling rate.