For adaptive filters with many taps, a short processing delay, and relative low computational complexity, the partitioned block frequency-domain adaptive filter (PBFDAF) is a good choice. The computational complexity of this algorithm is significantly reduced by using the alternated constrained PBFDAF. This particular algorithm applies gradient constraints in an alternating manner. In this paper, a serious problem in performance of the alternated constrained PBFDAF is described. Furthermore, a modification is proposed that effectively alleviates this problem. By using this modification together with a gradient constraint approximation, a new efficient alternated constrained PBFDAF is developed. Compared with the fully constrained PBFDAF, this new constraining method does not show any significant performance loss and still has a much smaller computational complexity.