This paper describes a terrain avoidance control methodology for autonomous rotorcraft applied to low altitude flight. A simple nonlinear model predictive control (NMPC) formulation is used to adequately address the terrain avoidance problem, which involves stabilizing a nonlinear and highly coupled dynamic model of a helicopter, while avoiding collisions with the terrain as well as preventing input and state saturations. The physical input saturations are made intrinsic to the model, such that the control is always admissible and the MPC design is simplified. A comparison of several optimization approaches is provided, where the performance of the traditional gradient method with fixed step is compared with the quasi-Newton method and a line search algorithm. The simulation results show that the adopted strategy achieves good performance even when the desired path is on collision course with the terrain.