Recent developments in electronics cooling imposed fin structures constructed from two materials ( e. g., copper and aluminum) as a thermo-economical solution for heat transfer enhancement. Such fins facilitate savings of expensive materials and reduce operating and investment costs by increasing efficiency. This paper stresses the importance of constraints on the geometrical optimization of "cascaded" fins made from two materials. Two types of constraints are analyzed in a unitary way: fixed weight ( relevant to aerospace and transportation applications) and fixed investment cost. The cascaded fin geometry springs from the thermal performance maximization under constraints (constructal principle). To illustrate the design principle and derive its fundamental features, it is sufficient to consider the most basic case of one-dimensional heat conduction through rectangular-rectangular, rectangular-triangular, and rectangular-parabolic cascaded fins. The study reveals that the ideal/theoretical limit of heat transfer enhancement obtained with a cascaded fin, with respect to an optimal-profile rectangular fin made in one single material, is about 15%. Additional effects like contact resistance at the interface between the two materials and the variation of heat transfer coefficient along the fins degrade the performance of the cascaded fin. However, even for relatively high contact resistances, cascaded fins can remain slightly superior to single material fins.