Shape-memory alloys (SMAs) are used as sensors and actuators in most engineering and medical applications and are optimized to exhibit either high stress recovery or high strain recovery. But most binary and ternary Cu-base SMAs are brittle and show low strain recovery due to the coarse grains obtained during solidification. Many new methods, such as powder metallurgy, rapid solidification, multipass rolling and equal-channel angular extrusion, are now being used to produce Cu-base shape-memory alloys with fine grains. However, these methods usually yield the alloys in small quantities despite the fact that each of them has its own advantages and limitations. Casting continues to be the most common and easiest method that helps produce SMAs in large quantities. To overcome the formation of coarse grains during casting, grain-refining additions were made to the liquid alloy. But the extent of grain refining achieved and, in turn, its effect on the shape recovery strain, varies from one study to another. The present work shows that by very small additions of Zr and Ti to a CuZnAl SMA with a low Al content, the shape-recovery strain can be increased to as high as 8%. The alloy also shows higher hardness and ductility after grain refinement.