During the late Precambrian and early Paleozoic, Laurentia and Baltica moved at minimum drift rates of up to 23 cm/yr. These drift rates are computed from paleomagnetic apparent-polar-wander paths and represent minimum velocities, because there could have been significant undetected longitudinal motion. A pronounced burst in latitudinal velocity followed the breakup of the supercontinent Rodinia, which had been assembled for about 400-500 m.y. Finite-element models with tectonic plates show that the presence of deep continental roots can strongly influence the velocity of continents if the driving source of buoyancy is located in the lower mantle. When plates are driven by lithospheric cooling and subducted slabs, the presence of a root is less important. We argue that Laurentia and Baltica were either pushed off of a hot lower-mantle source or pulled toward cold lower-mantle anomalies and that the presence of continental roots enhanced this motion.