We report a comparison of the specific-heat measurements on isoelectronic Cu-Zn-Al shape-memory alloys in the parent cubic phase L21 and in the close-packed martensitic phase 18R. Measurements were made by thermal-relaxation calorimetry over the temperature range 1.9 T 300 K. For the close-packed martensitic phase we find that the specific heat behaves similarly to that of pure copper which is also close packed. However, we observe deviations from Debye behavior for the cubic phase at low temperatures. This deviation is accounted for by the addition of 5% of Einstein localized modes to the Debye modes. Although the microscopic origin remains unknown, it was anticipated that it is related to the well-known softening of the TA2 110 phonon branch. In order to address this hypothesis an analysis of the lattice heat capacity of the cubic phase was compared to the calculated lattice heat capacity of -brass, as determined by integrating over the phonon density of states. A similar comparison was made between the close-packed phase and -brass.