We have tested a method originally developed by Beisser et al. (1990) to retrieve the source parameters (strike, dip, rake, and depth) of sparsely recorded earthquakes from the inversion of teleseismic waveform data. The complete wave train of all body waves is modeled using the reflectivity method. The parameter space of strike, dip, and rake is searched to find the source orientation which leads to the minimum misfit between the observed and the synthetic seismogram. The 1983 Kaoiki, Hawaii, earthquake (MS=6.6) was chosen as a test case. The inversion of the full data set (16 stations) gave a fault plane solution similar to the best double couple moment tensor solution of Harvard University and National Earthquake Information Centre. These three solutions were averaged to create a standard solution. Sparse data sets were simulated by decimating the full data set, and the resulting fault plane solutions were compared with the standard. We found that as few as one to three stations were sufficient to retrieve the focal mechanism of the 1983 Kaoiki event. We applied this technique to the 1951 Kona, Hawaii, earthquake (MS=6.9). A total of four stations and nine components were used to model the source parameters of this earthquake. The depth was estimated at 13¿3 km. The fault plane solution was a decollement type with a near-horizontal plane dipping at about 15¿ to the southwest and a near-vertical plane striking NW-SE. This observation supports a tectonic model for the Kona coast similar to that of Kilauea's south flank; the upper crust is pushed away from the center of Hawaii, slipping westward along a near-horizontal plane of weakness. ¿ American Geophysical Union 1994