A subset of 1961 earthquakes recorded during 1976-1993 by stations of the Central Mississippi Valley Seismic Network (CMVSN) was relocated using the JHD technique with constraints. These constraints were derived from the analysis of a subset of 246 earthquakes recorded simultaneously by the CMVSN and a portable network (PANDA) in 1989-1992. Because the PANDA stations targeted events in the central arm of the New Madrid seismic zone, only CMVSN events that occurred in the vicinity of this area were relocated. In addition, the stations used in the relocation were either within the embayment or outside of it but close to its edge. The one-dimensional velocity model used in the relocation includes a low-velocity layer corresponding to the unconsolidated embayment sediments. The constrained relocation has two major steps. The first one involved the joint location of the CMVSN/PANDA subset, with PANDA earthquake locations and station corrections fixed. The second step involved the joint location of the CMVSN subset with some locations and some station corrections fixed (as determined in the first step). To reduce the errors in the locations, only those earthquakes with maximum azimuthal gaps of less than 180° and final RMS residuals of 0.3 s or less in the last iteration were relocated. This decreased the number of earthquakes to 1015. To estimate the location errors, the earthquakes having fixed locations (90 events) were relocated using a single-event location program and the station corrections generated in the second step. Comparison of the new and original locations show average differences (in absolute value) in epicenter and depth of 0.6 and 1.0 km, respectively, although for some earthquakes the depth differences are much higher. Comparison of the JHD locations with the original catalog locations shows that, on average, the absolute values of the differences in epicenters and depths are equal to 0.9 and 1.7 km, respectively. The differences between the two sets of locations are fairly random. Although the new locations represent a substantial improvement over the original ones, particularly in depth, the former do not have the same quality as the PANDA JHD locations. An important result of our study is that the JHD technique detected the presence of arrival times corresponding to S-to-P converted waves that were misidentified as direct S-waves. This conversion is corroborated by comparison of PANDA and CMVSN seismograms for common events. The JHD S-wave station corrections compensated for this misidentification.