Our acoustic to articulatory inversion method exploits an original articulatory table structured in the form of a hypercube hierarchy. The articulatory space is decomposed into regions where the articulatory-to-acoustic mapping is linear. Each region is represented by a hypercube. The inversion procedure retrieves articulatory vectors corresponding to an acoustic entry from the hypercube table. A dynamic procedure is used to recover the best articulatory trajectory according to a minimum articulatory effort criterion. The inversion ensures that inverse articulatory parameters generate original formant trajectories with a very good precision, but not that they are realistic from a phonetic point of view. This papers shows how additional simple articulatory constraints can be incorporated in the inversion process. Constraints are implemented in the form of bonus attached to the points which verify the constraints imposed. This enables the inversion to be guided towards more realistic inverse articulatory trajectories.