Closed or nearly closed regions are an important form of perceptual structure arising both in natural imagery and in many forms of human-created imagery including sketches, line art, graphics, and formal drawings. We have developed a fast and effective algorithm especially suited for finding perceptually salient compact closed region structure in hand-drawn sketches and line-art. Starting with a graph of curvilinear fragments linked end-to-end with neighbors, the key problem is to manage the search of possible path continuations through junctions in an effort to find paths satisfying global criteria for closure and figural salience. We identify constraints on the ways that junctions arise in line drawings that permit effective guiding and pruning of search.