This article presents and illustrates several important subset design approaches for Gaussian nonlinear regression models and for linear models where interest lies in a nonlinear function of the model parameters. These design strategies are particularly useful in situations where currently-used subset design procedures fail to provide designs which can be used to fit the model function. Our original design technique is illustrated in conjuction with D-optimality, Bayesian D-optimality and Kiefer's Φk-optimality, and is extended to yield subset designs which take account of curvature.