Controls based on solutions to the state-dependent Riccati equation (SDRE) have been shown to offer high performance, but they suffer from unproven stability properties. This paper combines SDRE with satisficing, a novel clf-based approach which analytically guarantees stability. Essentially, the SDRE controller is projected point-wise onto the satisficing set. It is shown that this projection onto a stabilizing set in the control space can be solved analytically, and an example demonstrates the performance of the resulting SDRE-satisficing controllers.