This paper describes the optimization of a piezoelectric-driven synthetic jet actuator based on a Lumped Element Modeling (LEM). To simplify the problem, this papers splits the optimization problem into two parts. First, a constrained optimization of the cavity volume and orifice dimensions of two baseline synthetic jets, each with a given piezoelectric diaphragm, is conducted using two different objective functions. One seeks to improve the centerline output velocity over a broad frequency range, and the other maximizes the centerline velocity at a prescribed resonant frequency of the device. Significant improvements are achieved using both objective functions for both synthetic jets. Second, the two baseline piezoelectric diaphragms have been optimized using two configurations. One uses the standard inner-disc piezoceramic patch bonded to a metal shim, while the other employs an outer piezoceramic ring. In each case, the objective is to maximize the achievable volume displacement of the diaphragm at the coercive electric field strength of the piezoceramic, while the natural frequency of the piezoelectric diaphragm is constrained to be greater than or equal to the baseline designs. Both configurations yield modest (~5%) improvements for one diaphragm and significant improvements for the other diaphragm (>50%).