In 1997, Accot and Zhai presented seminal work analyzing the temporal cost and instantaneous speed profiles associated with movement along constrained paths. Their work posited and validated the steering law, which described the relationship between path constraint, path length and the temporal cost of path traversal using a computer input device (e.g. a mouse). In this paper, we argue that the steering law fails to correctly model constrained paths of varying, arbitrary curvature, propose a new form of the law that accommodates these curved paths, and empirically validate our model.