Take a strip of paper and fold a crease intersecting the long edges, creating two angles. Choose one edge and consider the angle with the crease. Fold the opposite edge along the crease, creating a new crease that bisects the angle. Fold again, this time using the newly created crease and the initial edge, creating a new angle along the chosen edge. It is well known that the angles thus constructed approach a limiting value independent of the initial angle. In this article, we generalize this process relaxing the requirement that the long edges be straight and that the folds be angle bisectors.