A coordinated Satellite Laser Ranging campaign was conducted in late 1996 to collect tracking data for two Global Positioning System satellites, designated as GPS-35 and GPS- 36. These satellites were equipped with laser retroreflectors to provide an independent means of tracking and verifying GPS ephemeris accuracy. Historically, GPS SLR data has been too sparse to determine an accurate SLR- derived reference orbit. Previous investigations have been limited to reporting SLR range residuals which were computed by comparing to GPS ephemerides. The present investigation benefits from two innovations. The first is the addition of the Naval Research Laboratory laser ranging system at the USAF Starfire Optical Range, which provided enough additional tracking data to make precision orbit determination possible. The second is the use of a sequential filter-smoother to process the SLR data instead of the batch least squares orbit determination methods employed in earlier investigations. A filter-smoother combines the best features of short arc and long arc estimation methods, optimizing the solution for each track of data. In this application the 3D solution is most accurate over each laser ranging site. The filter-smoother generates a continuous solution with variable accuracy, and provides a covariance which characterizes that accuracy. In this study we have verified the 3D accuracy of GPS ephemerides to within 10 cm, 30 cm, 12 cm (radial, intrack, crosstrack) over selected SLR sites using an SLR-only solution. These results were achieved with very little tracking data. Additional results are provided which indicate sensitivities to tracking geometry, average monthly tracking rates, and to track duration.