Many researchers have dealt with potential selectivity bias in developing country wage equations by employing Heckman's (1979) two-step method or related techniques, despite the potential for such methods to produce misleading results if the assumptions on which they are based are incorrect. This paper argues that the results produced even by parametric, easy-to-implement selectivity bias-correction methods can inspire more confidence than the typical applications to date when model selection testing is used to select (from a specified, diverse set) assumptions for which there is support in the data, and when sensitivity analysis is used to identify parameters whose estimates are robust across a wide range of assumptions. In particular, it highlights the importance of allowing for (the nonlinearities implied by) selection rule heteroskedasticity. There is economic reason to suspect heteroskedasticity and econometric reason to believe that the nonlinearities it introduces into the first stage will improve the performance of two-stage estimators. In an application to urban Peru, homoskedasticity is strongly rejected, and, in models allowing for heteroskedasticity, selection rule normality is no longer rejected, and estimates of key parameters become more robust to changes in other statistical assumptions. Because the nonlinearities appear to be captured well by the inclusion of quadratic terms in the first stage, the results suggest that researchers may have much to gain by including quadratic terms in standard probit selection rule estimation.