This study investigates the use of constraints upon articulatory parameters in the context of acoustic-to-articulatory inversion. These speaker independent constraints, referred to as phonetic constraints, were derived from standard phonetic knowledge for French vowels and express authorized domains for one or several articulatory parameters. They were experimented on in an existing inversion framework that utilizes Maeda's articulatory model and a hypercubic articulatory-acoustic table. Phonetic constraints give rise to a phonetic score rendering the phonetic consistency of vocal tract shapes recovered by inversion. Inversion has been applied to vowels articulated by a speaker whose corresponding x-ray images are also available. Constraints were evaluated by measuring the distance between vocal tract shapes recovered through inversion to real vocal tract shapes obtained from x-ray images, by investigating the spreading of inverse solutions in terms of place of articulation and constriction degree, and finally by studying the articulatory variability. Results show that these constraints capture interdependencies and synergies between speech articulators and favor vocal tract shapes close to those realized by the human speaker. In addition, this study also provides how acoustic-to-articulatory inversion can be used to explore acoustical and compensatory articulatory properties of an articulatory model.