The use of shifted Laplacians has become a popular method for preconditioning linear systems coming from the discretization of time-harmonic wave equations. In this talk, we analyze a multilevel Shifted Laplacian procedure that uses polynomial-based smoothers. The analysis reveals both strengths and limitations to the shifted Laplacian idea. Motivated by this analysis, we then propose an additional two-grid error correction step that can be used to further accelerate the convergence of the Shifted Laplacian preconditioner. This correction term is based on a projection of the original Helmholtz operator. Preliminary results indicate that the augmentation can not only improve the convergence but reduce the overall solve time for two and three dimensional problems.