Implications and improvements of edge brightening effects led by Q factor minimization restricted to keep the same level of directivity for high efficiency continuous circular aperture distributions are here reported. In this manner, an optimization strategy for a minimum Q value-keeping the same level of efficiency and restricting the maximum sidelobe level (SLL)- is envisaged. As application of the method, a design procedure devoted to reduce the Q factor of the antenna aperture distributions while keeping a high level of efficiency is outlined. Then, these optimal Taylor distributions are used as initial point to develop an optimization strategy. This procedure is devoted to search Taylor-like distributions which offer a good compromise ...