Application of the method of Joint Hypocenter Determination (JHD) to carefully determined arrival time data from a small network of sensitive and well-distributed local and teleseismic stations provides very precise locations of deep earthquakes. The precision of locations attained by this method-- the relative locations are good to about 5 km-- is limited mainly by the accuracy and precision of the measurements of arrival times. Application of the technique to a small and very active part of the deep earthquake zone of the Tonga island arc (depths near 600 km) reveals probable fault planes associated with the occurrence of deep earthquakes. The spatial distribution of precisely relocated hypocenters is closely related to the orientation of the focal mechanism solutions of two deep earthquakes. Hypocenters cluster in a plane parallel to one of the nodal planes for each of the two solutions examined. The plansa features are vearly vertical and have linear dimensions of about 40 km. In one case the shocks defining the fault plane also tended to cluster in time near the occurrence of the largest event. These and other data suggest the existence of several distinct fault planes in the area studied. Our study is being extended to examine the structure of the entire Tonga deep seismic zone.