This paper is devoted to the determination of the effectiveness and the optimization of two-dimensional (2-D), longitudinal rectangular composite fins under convective conditions through the concept of relative inverse thermal admittance. The influence of composite layer thickness and the composite and fin thermal conductivity ratio on the optimum geometry is determined. Effectiveness is used as the fundamental parameter to prove that the fin is fulfilling the objective of increasing heat dissipation. Once the optimum thickness has been obtained, the Biot number and the effectiveness are easily calculated. The optimization process is carried out through universal graphs in which the range of parameters covers most of the practical cases a designer will find and ensuring fins operate as a real dissipation device.