Until now there have been no reports of design techniques that include a means for developing pumps that can pump against higher pressure loads at the cost of less volume flow rate delivered to the load or vice versa. We address this problem for membrane micropumps that incorporate no-moving-parts valves (NMPV). A design approach is presented that utilizes a linear low-order model, finite element analysis to optimize piezoelectric actuation, and an algorithm to interrogate a design space of membrane thickness and valve size for any specified pressure load. The results indicate that optimum designs are relatively far from existing pumps and that significant improvements are possible. These gains appear to be due to the ability of the design approach to select non-obvious combinations of membrane stiffness and valve size to better “tune” the system, which is crucial in the case of NMPV pump, because excellent resonant behavior can make up for the fact that the valves do not open and close. Another important observation was that the optimal design point for pressure was not the same as for flow. This result is an indication that pumps can be designed for pressure or flow through careful design.