Speech production involves some of the most precise and finely timed patterns of human movement. Here, in the context of jaw movement in speech, we show that spatial precision in speech production is systematically associated with the regulation of impedance and in particular, with jaw stiffness. We estimated stiffness and also variability during movement using a robotic device to apply brief force pulses to the jaw. Estimates of stiffness were obtained using the perturbed position and force trajectory and an estimate of what the trajectory would be in the absence of load. We estimated this "reference trajectory" using a new technique based on Fourier analysis. A moving-average (MA) procedure was used to estimate stiffness by modeling restoring force as moving average of previous jaw displacements. The stiffness matrix was obtained from the steady-state of the MA model. We applied this technique to data from 31 subjects whose jaw movements were perturbed during speech utterances and kinematically matched non-speech movements. We observed systematic differences in stiffness over the course of jaw lowering and raising movements that were correlated with measures of kinematic variability. Jaw stiffness was high and variability was low early and late in the movement when the jaw was elevated. Stiffness was low and variability was high in the middle of movement when the jaw was lowered. Similar patterns were observed for speech and non-speech conditions. The systematic relationship between stiffness and variability points to the idea that stiffness regulation is integral to the control of orofacial movement variability.