This study uses Social Security earnings records matched to recent cross-sections of the SIPP and CPS to study the earnings progress of U.S. immigrants.The data show that immigrants' earnings grow 10 to 13 percent during their first twenty years in the U.S. relative to the earnings of natives with similar labor market experience. By comparison, estimates of immigrants' relative wage growth from cross-sections of the decennial Census are substantially higher. The divergent results reflect the selective outmigration of low--earning immigrants. The longitudinal earnings histories also show that 14 percent of immigrants have earnings in the U.S. prior to their most recent date of arrival, which points to a significant amount of back-and-forth migration between the U.S. and immigrants' home countries. The misclassification in previous work of these largely low-wage immigrants as recent arrivals accounts for close to one-third of the measured decline in the level of earnings of immigrant arrival cohorts between 1960 and 1980. The new evidence presented here, therefore, suggests that previous analyses had overestimated both the rate of earnings growth among immigrants who remain in the U.S. and the secular decline in the level of earnings across arrival cohorts.