We present a relatively simple motion-planning algorithm for a line segment (a "ladder") moving in 2-dimensional space amidst polygonal obstacles. The algorithm runs in time O(n2log n), where n is the number of obstacle corners, and is shown to be close to optimal. The algorithm is an optimized variant of the decomposition technique of the configuration space of the ladder, due to Schwartz and Sharir (Comm. Pure Appl. Math.36 (1983), 345-398; Advan. Appl. Math.4 (1983), 298-351; Robotics Res.2(3) (1983), 46-75). The optimizing approach used in our algorithm may be exploited to improve the efficiency of existing motion-planning algorithms for other more complex robot systems.