Using Co35Ni35Al30 (at.%) single crystals, the effects of crystals' axis orientation and ageing at 673 K for 0.5 h in free state on superelasticity responses in compression are investigated. Ageing of these single crystals is found to result in strengthening of the high-temperature B2 phase and L1(0) martensite, twofold increasing of temperature interval of SE response, and weakening of the orientation dependence and improving of the cycle stability of superelasticity response. In [011]- and [123]-oriented single crystals the values of the stress hysteresis decrease nearly threefold as compared to the quenched state. The combination of high-strength [001] crystal axis orientation and precipitation of coherent nanoscale particles leads to the best stability of SE response in aged Co35Ni35Al30 single crystals.