Shape memory alloys undergo reversible transformations between two distinct phases in response to changes in temperature or applied stress'. The creation and motion of the internal interfaces between these phases during such transformations dissipates energy, making these alloys effective mechanical damping materials(2,3). Although it has been shown that reversible phase transformations can occur in nanoscale volumes(4-9), it is not known whether these transformations have a sample size dependence. Here, we demonstrate that the two phases responsible for shape memory in Cu-Al-Ni alloys are more stable in nanoscale pillars than they are in the bulk. As a result, the pillars show a damping figure of merit that is substantially higher than any previously reported value for a bulk material, making them attractive for damping applications in nanoscale and microscale devices.