Although Cu-based shape-memory alloys possess higher transformation temperatures compared with Ni-Ti shape-memory alloys and a higher magnitude of strain recovery, they are still not used extensively in commercial applications since they suffer from some inherent drawbacks, such as a lack of ductility and stabilization of martensite. Cu-Zn-Al alloys in particular are more prone to stabilization. In the present work, therefore, a Cu-Zn-Al alloy with a low Al content (<3 wt%) prepared by ingot metallurgy was thermally processed by subjecting it to different quenching treatments, such as direct quenching, up-quenching and step-quenching using water, oil and brine solution as the quenchants. The effect of different methods of quenching as well as the quenchants themselves on the microstructure, transformation temperatures and shape-memory characteristics of the alloy was investigated and the results obtained have been interpreted. The study reveals that quenching in a brine solution results in 100% martensite, thereby getting rid of the deleterious effects of aging. The characteristic transformation temperatures are also modified by variations in the rate of quenching.