Some results concerning the martensite stabilization in Cu-Zn-Al single crystals with e/a = 1,48 and with certain distributions of gamma precipitates are presented. After several aging periods in martensite, the stabilization is reduced (practically eliminated) in samples containing precipitates when compared to the behavior of precipitate-free samples subjected to a step-quench type thermal treatment which is known to be effective in reducing the stabilization in copper-based shape memory alloys.