Small earthquake records are increasingly being used as empirical Green's functions to estimate the source time functions (STFs) of large earthquakes. This is generally accomplished in the frequency domain by computing the ratio of the large to the small event spectrum and then transforming it back to the time domain. When the data quality is poor, the resulting STFs often show unrealistic long-period signal and short-period oscillation. In this study we propose an alternative method in which a large-event STF is approximated by a series of pseudotriangular pulses whose parameters are determined by a nonlinear frequency-domain inversion, involving the spectrum of the large and the small events. The method allows a “positivity” constraint to be imposed on the STF. The misfit between the observed and computed large-event seismograms is measured in the frequency domain over the range of frequency in which the data are reliable. We present tests of the method on synthetic data and on earthquake records from Mexico, both of which show the robustness of the method. The quality of the solution is dependent on the quality of the input data. As the input data become more bandlimited and more noisy, the reliability and usefulness of the solution will decrease.