Shape memory Cu-Al-Ni single crystals of two alloy compositions Cu 82.5 wt.% - Al 13.5 wt.% - Ni 4.0 wt.% and Cu 81.98 wt.% - Al 14.02 wt.% - Ni 4.0 wt.% have been studied in view of their ability to undergo spontaneous jumping during reverse martensitic transformation. Crystals of both alloys were compressively deformed up to a full shape memory strain (8%) at room temperature. It was found that specimens of the first alloy with martensite structure jumped higher and demonstrated better reproducibility in cyclic tests. The height of the jump strongly depended on thermal pre-treatment and was unaffected by the strain rate during pre-strain by compression and the heating rate at shape recovery.