This paper addresses tradeoffs between pressure sensitivity and electronic noise floor in optimizing the performance of a piezoresistive microphone. A design optimization problem is formulated to find the optimum dimensions of the diaphragm, the piezoresistor geometry and location for two objective functions: maximum pressure sensitivity and minimum electronic noise floor. The Pareto curve of optimum designs for both objectives is generated. The minimum detectable pressure (MDP) was also employed as an objective function, generating a point on the Pareto curve that may be the best compromise between the original two objectives. The results indicated that this application the critical constraints are the linearity and power consumption. The minimized MDP design was less sensitive to uncertainty in design variables. The optimization methodology presented in this paper as well as some of the conclusions are applicable to other types of piezoresistive sensors.