The hierarchical principle is discussed in perturbation theory in the light of the fact that Cutkosky integrals can have lower-order singularities corresponding to contracting out complete closed loops. It is shown that a strict hierarchical principle can be defined for Feynman integrals in theα-representation but that due to a hitherto overlooked mechanism identically located singularities occur at different levels in the hierarchy. The discussion is illustrated throughout by reference to the icecream-cone diagram.