The increased importance of heat sinks in electronic cooling applications has resulted in a revived interest in extended surfaces, or fins. Also, space and cost constraints provide impetus for optimizing thermal performance for a given, or least, amount of material. The current research focuses on a pin fin design of least material, where the diameter of the pin fin varies axially to maintain the axial heat flux constant; thus all fin material is utilized equally. Although such fins have been studied in the past, the convective heat transfer coefficient was assumed to be constant, which is not entirely true since it is known to be a function of diameter for cylindrical bodies. The current research shows that an optimal fin based on a variable convective heat transfer coefficient yields a true optimal profile, and utilizes material better; that is, it uses a lower volume of material to achieve the same heat dissipation rate. This improvement in material utilization is show to be anywhere from approximately 3% to 14%.