Conventional techniques used to design transducer apertures for medical ultrasound are generally iterative and ad-hoc. They do not guarantee optimization of parameters such as mainlobe width and sidelobe levels. We propose a dynamic aperture weighting technique, called the Minimum Sum Squared Error (MSSE) technique, that can be applied in arbitrary system geometries to design apertures optimizing these parameters. The MSSE technique utilizes a linear algebra formulation of the Sum Squared Error (SSE) between the point spread function (psf) of the system, and a goal or desired psf. We have developed a closed form expression for the aperture weightings that minimize this error and optimize the psf at any range. We present analysis for Continuous Wave (CW) and broadband systems, and present simulations that illustrate the flexibility of the technique.