Supporters of speech as an essentially motion phenomenon have forgotten the evidence, coming from static phases in the “elastic speech” flow, that these phases can give direct access to speech structures at their best. In fact the very name of this Structure-from-Motion (SfM) problem means that motion is just for recovering structures, when undersampled. By combining SfM with Multistable Perception, we will reinforce the claim that changes in the perceiver's mind, regarding stationary or repetitive audiovisual speech moving displays, are perceptual decisions on changes in structure, rather than simple low-level decisions on changes in motion direction. The outcome of this quest for speech structure recovery is that, contrary to other perception domains, where scientists are struggling in search of stabilizing biases, the very time unfolding of speech coordinations –and non-human primate calls– gives for free neural control biases within their natural integrative time-windows.