This paper proposes two modifications of the filtered-x least mean squares (FxLMS) algorithm with improved convergence behavior albeit at the same computational cost of 2M operations per time step as the original FxLMS update. The paper further introduces a generalized FxLMS recursion and establishes that the various algorithms are all of filtered-error form. A choice of the stepsize parameter that guarantees faster convergence and conditions for robustness are also derived. Several simulation results are included to illustrate the discussions.