This paper introduces an approximate adder architecture based on a digital quasi-feedback technique called Carry Cut-Back in which high-significance stages can cut the carry propagation chain at lower-significance positions. This lightweight approach prevents activation of the critical path, improving energy efficiency while guaranteeing low worst-case relative error. It offers a degree of freedom which allows to dissociate precision and dynamic range in fixed-point implementation. A design methodology is presented along with results and a comparative study. For a worst-case accuracy of 98%, energy savings up to 44% and power-delay-area reductions up to 62% are demonstrated compared to low-power conventional designs.