Abstract: We propose a weak condition of compatibility between phases applicable to cases exhibiting full or partial coherence and Widmanstätten microstructure. The condition is applied to the study of Sb2Te3 precipitates in a PbTe matrix in a thermoelectric alloy. The weak condition of compatibility predicts elongated precipitates lying on a cone determined by a transformation stretch tensor. Comparison of this cone with the long directions of precipitates determined by a slice-and-view method of scanning electron microscopy combined with focused ion beam sectioning shows good agreement between theory and experiment. A further study of the morphology of precipitates by the Eshelby method suggests that interfacial energy also plays a role and gives an approximate value of interfacial energy per unit area of 250 dyn cm−1.