Our goal is to recover articulatory information from the speech signal by acoustic-to-articulatory inversion. Like most inversion methods proposed in the literature, our method relies on the analysis-by-synthesis paradigm. After an overall description of the inversion method the paper presents how inversion can be used to investigate acoustic properties of the articulatory model, which helps us to formulate the way of incorporating effective constraints to obtain phonetically realistic inverse solutions. First, the inversion method has been applied to French vowels in order to study the dispersion of vocal tract shapes corresponding to each of these vowels. Second, in addition to increasing the intrinsic quality of the articulatory table, constraints can be incorporated directly in the dynamic programming stage to obtain more realistic inverse trajectories in a sequence of vowels. These constraints derive from phonetic knowledge, such as the observation of the strong protrusion for /y/, of a posterior place of articulation for /u/, of a strong mouth opening for /a/ and so on.