The radial orbit error has long been the major error source in ERS-1 altimetry, crippled by having only satellite laser ranging for precise tracking and relying on insufficiently accurate general-purpose gravity field models. Altimeter crossovers are used very effectively as additional tracking data to laser ranging. The ERS Tandem Mission even provides the unique possibility to simultaneously determine orbits of two similar satellites flying the same orbit. Altimeter crossovers between the two satellites then link the two orbits into a common reference frame. Tailoring of the Joint Gravity Model 3 (JGM 3) is another step to reduce orbit errors. This technique is aimed at the reduction of the geographically anticorrelated orbit error (observed in the crossover height differences) through the adjustment of selected gravity field parameters. The resulting Delft Gravity Model (DGM)-E04 has reduced this part of the orbit error by a factor of 2, performs even better with respect to the ESA-provided orbits, and also outperforms the recent Earth Geopotential Model EGM96 in this respect. ERS-1 and ERS-2 orbits for the entire Tandem Mission are computed and studied in detail, and orbit errors due to the gravity field and nonconservative forces are identified. Analyses systematically show that the orbits computed with JGM 3 have a radial root-mean-square orbit accuracy of 7 cm, with DGM-E04 5 cm. ¿ 1998 American Geophysical Union