Dedicated fan-duct-heatsink combinations have become a standard means of cooling computer processors. Most previous studies have considered optimization of fin geometry (pitch and thickness) with overall heatsink dimensions (width, height, length) fixed. The present study considers size requirements for the constraints of fixed air volume flow rate and pressure drop, fixed fan/blower power, and fixed thermal conductance. First, an ideal heatsink with infinite fin thermal conductivity is considered, providing simple power-law prediction of performance. Next, fins of finite thermal conductivity and thickness, as well as effects of developing flow are included in the analysis, permitting prediction and minimization of weight. Models of both levels of complexity can be used, previous to more detailed numerical and/or experimental studies, to design optimized heatsinks.