Fractional polynomial models are potentially useful for response surface investigations. With the availability of routines for fitting nonlinear models in statistical packages they are increasingly being used. However as in all experiments the design should be chosen such that the model parameters are estimated as efficiently as possible. The design choice for such models involves the usual difficulties of nonlinear models design. We find Bayesian optimal exact designs for several fractional factorial models. The optimum designs are compared to various standard designs in response surface problems. Some unusual problems in the choices of prior and optimization method will be noted.