When a model is nonlinear, bootstrap testing can be expensive because of the need to perform at least one nonlinear estimation for every bootstrap sample. We show that it may be possible to reduce computational costs by performing only a fixed, small number of artificial regressions, or Newton steps, for each bootstrap sample. The number of iterations needed is smaller for likelihood ratio tests than for other types of classical tests. The suggested procedures are applied to tests of slope coefficients in the tobit model, where asymptotic procedures often work surprisingly poorly. In contrast, bootstrap tests work remarkably well, and very few iterations are needed to compute them.