| This paper presents an online planner for suboptimal obstacle avoidance. It generates near-shortest paths incrementally by avoiding obstacles optimally one at a time. In known environments, obstacles are avoided in an order determined by a global criterion. In unknown environments, obstacles are avoided as they are detected by on-board sensors. This avoidance strategy is guaranteed to reach the goal regardless of the order in which the obstacles are avoided. The method is demonstrated in several examples for an omnidirectional point robot moving among planar polygonal obstacles.