The objective of the presentation is to examine issues in constraining acoustic-to-articulatory maps by means of facial data and other a priori knowledge regarding speech production. Constraints that are considered are the insertion of data on lip opening, spread and protrusion, as well as other facial data together with constraints on the vocal tract length. A priori knowledge that has been taken into account concerns the deformation and speed of deformation of the vocal tract as well as phonetic rules regarding vowel-typical tract shapes. Inverse maps that have been tested are formant-to-area and formant-to-parametric sagittal profile maps as well as audio/visualto- electromagnetic coil trajectory maps. The results obtained while mapping audio-only data compared to audio combined with other data are discussed.