The centroid-moment tensor inversion scheme of Dziewonski et al. (J. Geophys. Res., 86: 2825-2852, 1981) is complemented with a moving window analysis in the frequency domain to retrieve the smooth source spectrum of large earthquakes in the frequency range 2.25-11.5 mHz. Synthetic seismograms are constructed by normal mode summation and cross-correlated with the observed traces to retrieve the origin time delay and frequency dependence of the apparent centroid location. In addition to the source mechanism, the back-transformation of the source spectrum into the time domain enables us to recover a smooth version of the source time function. The low-frequency parameters are subsequently checked by partitioning the source time function into two sub-events of equal size and duration and by looking for the location of the second sub-event that best fits the waveform of the signals over the entire frequency range. This doublet approach can retrieve the spatial information of the source more reliably than the centroid approach. The method allows for a careful check of all possible trade-offs between source parameters. In particular, we illustrate the trade-offs arising between directivity and source amplitude spectrum, and the importance of constrained inversions in source mechanism studies.