I adapt the Generalised Method of Moments to deal with nonlinear models in which a finite number of isolated parameter values satisfy the moment conditions. To do so, I initially study first-order underidentified models whose expected Jacobian is rank deficient but not necessarily 0. In both cases, the proposed procedures yield efficiency gains and underidentification tests with standard asymptotics. I study separately non-linear in parameters but linear in variables models and fundamentally non-linear models without separation of data and parameters. I illustrate the proposed inference procedures with a dynamic panel data model and a non-linear regression model for discrete data.