The TANAMI program monitors southern hemisphere gamma-ray loud AGN.Parsec scale imaging enables the measurement of brightness temperatures, opening angles and velocities of AGN jets, constraining their orientation, Doppler and bulk jet Lorentz factors. TANAMI is well poised for the imminent CTA era, as its current sample includes a number of TeV objects, and more such sources are being added. Our monitoring can track ejections of new jet features in AGN studied with the CTA and find correlations with high-energy variability. Here we present results from a multi-epoch study of TeV blazars that belong to the AGN sub-class of high-frequency peaked BL Lac objects, known to produce bright and violently variable gamma-ray emission at TeV energies. We find a broad range of jet velocities from stationary or slow features to apparently superluminal motions up to 8c. Considering all published measurements of TeV blazar jet velocities, high apparent superluminal motion is clearly less common than in more powerful quasars. However, the growing distribution now shows a tail up to considerable high speeds which has implication for the so-called Doppler Crisis: the discrepancy between high Doppler and bulk Lorentz factors inferred from gamma-ray studies and the lower values determined from radio VLBI observations.