Though Ni–Ti shape memory alloys are used extensively in a variety of engineering and medical applications because of their attractive shape memory characteristics, they still suffer from certain drawbacks, such as low transformation temperatures, difficulty in production and processing and high cost of raw materials. Copper-based alloys have, therefore, come as an alternative to Ni–Ti shape memory alloys. They are easier to produce and process and are also less expensive. They are used where Ni–Ti alloys cannot be used. But Cu–Al–Ni shape memory alloys also pose problems since they are brittle and possess lower shape recovery strains and stresses. With a view to increasing the shape memory characteristics and ductility of Cu–Al–Ni shape memory alloys, they were subjected to grain refinement and thermomechanical processing. The present study establishes that grain-refining additions result in considerable reduction in the grain size of the alloys. In addition, grain refinement and alloying cause an increase in the transformation temperatures. The results are analysed in the light of the explanations/theories put forth in recent papers related to Cu–Al–Ni shape memory alloys, and an attempt has been made to compare the results.