n the context of shape matching, this paper proposes a framework for selecting the Laplacian eigenvalues of 3D shapes that are more relevant for shape comparison and classification. Three approaches are compared to identify a specific set of eigenvalues such that they maximise the retrieval and/or the classification performance on the input benchmark data set: the first k eigenvalues, by varying k over the cardinality of the spectrum; the Hill Climbing technique; and the AdaBoost algorithm. In this way, we demonstrate that the information coded by the whole spectrum is unnecessary and we improve the shape matching results using only a set of selected eigenvalues. Finally, we test the efficacy of the selected eigenvalues by coupling shape classification and retrieval.