A high sensitivity microcalorimeter is described which is capable of carrying out measurements on samples subjected to uniaxial tensile stress. This novel calorimeter was used, together with stress-free calorimetry, to map the composition dependence of the martensite phase-stabilities in four Cu-Al-Ni alloys. It is shown that stress-temperature phase diagrams produced using this approach are extremely interesting since they contain phase boundaries which were previously inaccessible during stress-induced transformation experiments. Direct calorimetric determinations of the enthalpy and entropy changes during B> -> 7' transformation are also presented for the four alloys, and the effect of applied stress on the enthalpy and entropy changes during both 13 -* y', and 6 -> 15' transformation are analysed for one of the alloys.