Given an oval C in the plane, the α -isoptic C α of C is the plane curve composed of the points from which C can be seen under the angle π - α . We consider isoptics of ovals parametrized with the support function p ( t ) = a + cos n t , n ∈ N , and present an example of an oval such that when α increases, the α -isoptics begin to be convex, then lose their convexity and finally are convex again along a curve intersecting the isoptics orthogonally. Next we give an example of a curve from the same family, for which the curvature of the isoptics changes its sign three times. These changes occur on the symmetry axes of the oval C and coincide with the orthogonal trajectories which start at the points with extremal curvature. Finally, we formulate the hypothesis concerning the general case where we expect n - 1 convexity limit angles for the isoptics of an oval parametrized by p ( t ) = a + cos n t .