Leakage losses and ever-increasing power dissipation in the microprocessor are causing significant thermal, mechanical, and reliability problems. Conventional cooling methods are reaching their practical limits, and new methods of lowering the operating temperature of microprocessors are being explored. Microfluidics-based cooling schemes are one approach being considered. The implementation of microchannels for forced convection at the chip level shows much promise, as the effective heat transfer surface area and attainable heat flux are very favorable. A major design limitation to such an implementation is the pressure developed within such micro-flows and the stresses that could result. In this study, multiple discrete microchannel heat sink configurations are analyzed computationally and compared in a cooling capability sense, while total pressure drop across the flows is carefully considered. A single cooling channel over an energy source is split into two smaller channels, and so on, while total pressure drop is maintained constant, and specified such that all flows remain in the laminar regime. It is shown that for the configurations analyzed, there exists multiple-dependence optimum cooling configurations. In addition, it is shown that a slimmer design may be implemented with a relatively small effect on cooling capability. Furthermore, cooling capability dependence on total pressure drop of the flows is shown to be minimal for high-performing microchannel configurations.