Does the speech motor control system use invariant vocal tract shape targets when producing vowels and semivowels? A 4-part theoretical treatment favoring models whose only invariant targets are regions in auditory perceptual space over models that posit invariant constriction targets is presented. Auditory target regions are hypothesized to arise during development as an emergent property of neural map formation in the auditory system. Furthermore, speech movements are planned as trajectories in auditory perceptual space. These trajectories are then mapped into articulator movements through a neural mapping that allows motor equivalent variability in constriction locations and degrees when needed. These hypotheses are illustrated using computer simulations of the DIVA model of speech acquisition and production. Finally, several difficult challenges to proponents of constriction theories based on this theoretical treatment are posed.