It is often believed that without instruments, endogenous sample selection models are identified only if a covariate with a large support is available (see, e.g., Chamberlain, 1986, Journal of Econometrics 32, 189–218; Lewbel, 2007, Journal of Econometrics141, 777–806) . We propose a new identification strategy mainly based on the condition that the selection variable becomes independent of the covariates for large values of the outcome. No large support on the covariates is required. Moreover, we prove that this condition is testable. We finally show that our strategy can be applied to the identification of generalized Roy models.