This paper presents an efficient adaptive algorithm for designing FIR digital filters that are efficient according to an Lp error criteria. The algorithm is an extension of Burrus' iterative reweighted least-squares (IRLS) method for approximating Lp filters. Such algorithm will converge for most significant cases in a few iterations. In some cases however, the transition bandwidth is such that the number of iterations increases significantly. The proposed algorithm controls such problem and drastically reduces the number of iterations required.