Disparate behaviour of above-the-step quantal reflection probability for smooth and composite semi-infinite potentials is shown. For a smooth semi-infinite potential (step) the reflectivity is usually a monotonically decreasing function of energy. But the composite two-piece (non-differentiable, e.g., at x = 0) potential step gives rise to a parameter-dependent pronounced single minimum in the reflectivity. Three analytically solvable and several other models of composite semi-infinite (step) potentials are shown supporting such a behaviour of the quantal reflection.