Three-component seismic waveforms recorded at the single broadband station SJG have been examined for four MW ≥ 6 Caribbean earthquakes using a regional moment-tensor (RMT) inversion procedure that uses a general crustal velocity model to generate synthetic Green's functions at a fixed depth. Comparisons of the computed source parameters with solutions reported by international agencies indicate that the RMT procedure provides a rapid estimate of the earthquake magnitude using a single station. Focal mechanisms are not as well resolved and may require a more complete azimuthal coverage. The inversion procedure thus provides a timely estimate of the earthquake magnitude that would be useful for tsunami alerting. Warning intervals for the Caribbean region would vary from about 12 minutes for a tsunami generated at a distance of 200 km to more than 60 minutes for a tsunami originating at a distance of 800 km from the recording site.