Model Predictive Control (MPC) while being a very effective control technique can become computationally demanding when a large prediction horizon is selected. To make the problem more tractable, one technique that has been proposed in the literature makes use of control input parameterizations to decrease the numerical complexity of nonlinear MPC problems without necessarily affecting the performances significantly. In this paper, we review the use of parameterizations and propose a simple Sequential Quadratic Programming algorithm for nonlinear MPC. We benchmark the performances of the solver in simulation and compare them with state-of-the-art solvers. Results show that parameterizations allow to attain good performances with (significantly) lower computation times.