In order to explain the stabilised shape memory behaviour observed during the thermal and mechanical cycling of a Cu–14·86Zn–5·81Al–0·5Fe (wt-%) alloy, X-ray diffraction and optical microscopy studies have been performed. The former have shown that the previously reported reorientation of the α brass phase crystallites from α(111) to α(200), observed during the heating up to 500°C, also occurs during a complete heating–cooling cycle up to 325°C. Optical microscopy studies confirm the increasing tendency for α phase preferred formation when the temperature is increased from 325 to 500°C. This texturing effect that occurs during thermal cycling is accompanied by an increase in the amount of α phase with a reduction in the amount of β2 austenite. Finally, a tensile completely recoverable pseudoelastic strain of almost 0·6%, determined during a loading–unloading cycle applied to a heat treated specimen that contained no austenite, has been ascribed to the reversible formation of a specific martensite variant.