The effectiveness of a series of optically transparent aligners for orthodontic treatments depends on the anchoring of each tooth. In contrast with the roots, the crowns’ positions and orientations are measurable with intraoral scans, thus avoiding any X-ray dose. Exemplified by two patients, we demonstrate that three-dimensional crown movements could be determined with micrometer precision by registering weekly intraoral scans. The data show the movement and orientation changes in the individual crowns of the upper and lower jaws as a result of the forces generated by the series of aligners. During the first weeks, the canines and incisors were more affected than the premolars and molars. We detected overall tooth movement of up to about 1 mm during a nine-week active treatment. The data on these orthodontic treatments indicate the extent to which actual tooth movement lags behind the treatment plan, as represented by the aligner shapes. The proposed procedure can not only be used to quantify the clinical outcome of the therapy, but also to improve future planning of orthodontic treatments for each specific patient. This study should be treated with caution because only two cases were investigated, and the approach should be applied to a reasonably large cohort to reach strong conclusions regarding the efficiency and efficacy of this therapeutic approach.