While maximizing line-of-sight coverage of specific regions or agents in the environment is a well explored path planning objective, the converse problem of minimizing exposure to the entire environment during navigation is especially interesting in the context of minimizing detection risk. This work demonstrates that minimizing line-of-sight exposure to the environment is non-Markovian, which cannot be efficiently solved optimally with traditional path planning. The optimality gap of the graph-search algorithm A* and the trade-offs in optimality vs. computation time of several approximating heuristics is explored. Finally, the concept of equal-exposure corridors, which afford polynomial time determination of all paths that do not increase exposure, is presented.