In previous papers [Cummins et al., 1994ab> (hereafter referred to as DSMI and DSMII respectively), we presented accurate methods for computing complete synthetic seismograms for SH and P-SV respectively in a spherical earth model. The SH calculations used computationally efficient modified matrix operators, but the P-SV synthetics were computationally intensive. Geller and Takeuchi [1995> (hereafter referred to as GT95) presented a general theory for deriving modified operators and gave the explicit form of the modified operators for the P-SV case in cylindrical or cartesian coordinates. In this paper we extend GT95's results to derive modified operators for the P-SV case in spherical coordinates. The use of the modified operators reduces the CPU time by a factor of about 5 without a loss of accuracy. 10 CPU min on a SPARC-20 workstation with one CPU are required to compute a profile of synthetic seismograms from DC to 20 sec period. ¿ American Geophysical Union 1996