Alternating Sequential Filters (ASFs) rely on the iterated application of openings and closings of increasing strength. Since connected openings and closings can be designed from the component tree, it is possible to define Connected ASFs (CASFs) by alternatively pruning the branches of the dual max- and min-trees of an image. The main drawback of this approach is that pruning one of the trees modifies not only the image but also the dual tree. Recomputing a component tree at each iteration of the process is computationally expensive. In this article, we show how a component tree can be efficiently updated (avoiding reconstruction) when its dual tree is pruned. We build upon this algorithmic scheme to propose a computationally efficient CASF algorithm.