This paper follows an accompanying one on the constrained minimization of cam profiles with translating flat-face followers. Here, the corresponding problem for oscillating flat-face followers is addressed. The unconstrained optimization of this type of cam mechanisms, aimed at the minimization of the area of the cam disk, has been reported elsewhere. In this paper we recognize that unconstrained cam-size minimization can lead to profiles with curvature discontinuities, i.e.. cusps, which should be eliminated, for they give rise to inadmissibly large contact stresses. The conditions under which curvature discontinuities arise are derived. These conditions lead to a simple constrained minimization procedure, whose application is illustrated with a fully solved numerical example.