In prior studies paleomagnetic data have been used to determine ancient minimum velocities of the continents. The greatest minimum velocities, ~50km/m.y., exceed the present-day absolute velocities of the major continent. This result is important because the observation that present-day oceanic plates move faster than present-day continental plates can be treated as a major constraint on plate dynamics. However, these prior studies are limited because they ignore known errors in the paleomagnetic data. In this paper we present a technique for incorporating these errors and using them to estimate 95% confidence limits on the minimum velocities. This new technique was applied to Pennsylvania to Cretaceous paleomagnetic data from North America and to the ancient geometry og Laurasia. When errors are considered, minimum velocities are 10 to 50km/m.y. lower than when errors are ignored. Additional uncertainties owing to hypothesized clockwise rotation of the Colorado Plateau, a source of many of the data, are considered and found to alter the minimum velocities only negligibly. Allowing for uncertainties in the pole positions, uncertainties in ages, and the uncertainty due to possible rotation of the Colorado plateau, we estimate that Laurasia moved at least 48 km/m.y. from Early Jurassic to Early Cretaceous time, and at least 43 km/m.y. from Pennsylvanian through Late Triassic time. There is only a 5% risk that the true minimum velocities are lower than these lower bounds. These velociites are less than the peak velocities over short intervals found in prior analyses, but exceed the average velocities previously found for Triassic and Jurassic time. These newly estimated velocities are still much higher than the present velocities of the continents and, as in the prior studies, imply that the slow motion characteristic of major continents at present is not a fundamental attribute of plate motions.