Homological Perturbation Theory [11, 13] is a well-known
general method for computing homology, but its main algorithm, the Basic
Perturbation Lemma, presents, in general, high computational costs.
In this paper, we propose a general strategy in order to reduce the complexity
in some important formulas (those following a specific pattern)
obtained by this algorithm. Then, we show two examples of application
of this methodology.