In this paper we study the problem of finding a set of k directions for a given simple polygon P, such that for each point p ∈ P there is at least one direction in which the line through p intersects the polygon only once. For k = 1, this is the classical problem of finding directions in which the polygon is monotone, and all such directions can be found in linear time for a simple n-gon. For k > 1, this problem becomes much harder; we give an O(n ⁵log² n)-time algorithm for k = 2, and O(n ^3k + 2)-time algorithm for k ≥ 3. These results are the first on the generalization of the monotonicity problem.