Multilevel semantics has been proposed as a powerful architecture for semantic analysis. We propose a methodology that, while maintaining the generality of the multilevel approach, is able to establish formal constraints over the possible ways to organize the level hierarchy. More precisely, we propose a "strong" version of the multilevel approach in which a level can be defined if and only if it is possible to characterize a "meaningfulness" notion peculiar to that level. Within such an architecture each level reached during the analysis computes its meaningfulness value; this result is then handled according to modalities that are peculiar to that level. The component described in this paper was designed to be portable with respect to the application domain and so far has been tested as the semantic analysis component of two multimedial dialog systems, ALFresco and MAIA.