This paper examines the economic impact of the second great immigration wave (1945-2000) on the US economy. Contrary to recent studies, we estimate that immigration induced important net gains and small redistributive effects among natives. Our analysis relies on a computable general equilibrium model combining the major interactions between immigrants and natives (labor market impact, fiscal impact, capital deepening, endogenous education, endogenous inequality). We use a backsolving method to calibrate the model on historical data and then consider two counterfactual variants: a cutoff of all immigration flows since 1950 and a stronger selection policy. According to our simulations, the postwar US immigration is beneficial for all cohorts and all skill groups. These gains are closely related to a long-run fiscal gain and a small labor market impact of immigrants. Finally, we also demonstrate that all generations would have benefited from a stronger selection of immigrants.