Some Single-Microphone Speech Enhancement algorithms based on the iterative Wiener filtering Method due to Lim-Oppenheim [2] are evaluated. In the original Lim-Oppenheim algorithm, AR spectral estimation of speech is carried out using a second-order analysis, but our algorithms consider an AR estimation from a cumulant analysis. This work extends some preceding papers due to the authors [4], [5]. Third- and fourth-order cumulant-based algorithms are compared to classical second-order one. This comparison is evaluated by considering three different noisy environments. A detailed study based on a frame-by-frame analysis leads to an optimum iteration of each algorithm as a trade-off between noise reduction and distortion effects. Voiced and unvoiced sounds are separately discussed. We conclude that third-order cumulant-based algorithm offers a more valuable performance than the others.