This paper deals with a new adaptive step-size overlay dedicated to Least Mean-Square (LMS) algorithms for noise cancellation with reference. LMS algorithms are often used in real-time estimations due to their robustness and simplicity, and are guided by their constant step size. Their transient and asymptotic performances are both linked to the step size, which leads to the well-known trade-off between speed and accuracy. In this paper, we propose a LMS algorithm with a new self-adaptive overlay based on a Multiplicative Update with Forgetting Factor (LMS-MUFF). The adaptive overlay improves the speed and the reactivity of the algorithm. In order to tune the algorithm parameters, we express the scalar case semi-analytical relationship between the LMS-MUFF parameters and a false-alarm probability, as defined from unwanted variations in the step-size during the asymptotic mode. We compare our method to reference methods in the literature and show that it offers better speed and reactivity with the same asymptotic performance. Index Terms—least mean-square algorithms; adaptive noise cancellation algorithms; self-adaptive step size; steepest descent algorithms.