The problem of space-constrained absorbers in the low frequency range constitutes an area of continuous research. Micro-perforated panels are advantageous because they can be tuned by a proper selection of their constitutive physical parameters including the diameter of the perforations and their separation distance, their thickness and the length of the backing cavity. However, such optimal selection is not straightforward, especially when considering multi-layer partitions. Current optimization algorithms are based on the maximization of the total absorption coefficient averaged over a frequency band, that requires a compromise between the bandwidth and the thickness of the control device. In this work, the problem is analysed on the basis of a causality criterion. This principle is generalized from its formulation in the field of electromagnetism to obtain a relation that correlates the thickness-to-bandwidth performance of a micro-perforated absorber to its total absorption coefficient. Using this relation, an optimization procedure is presented for the sequential selection of the optimal physical parameters for single-layer partitions. An excellent agreement has been found between the optimal values obtained by the causality criterion and those achieved by critical coupling conditions.