In this work we present the generalization of the model for chain formation in break junctions, introduced by Thiess et al (2008 Nano Lett. 8 2144), to zigzag transition-metal chains with s and p impurities. We apply this extended model to study the producibility trends for noble-metal chains with impurities, often present in break junction experiments, namely, Cu, Ag and Au chains with H, C, O and N adatoms. Providing the material-specific parameters for our model from systematic full-potential linearized augmented plane-wave first-principles calculations, we find that the presence of such impurities crucially affects the binding properties of the noble-metal chains. We reveal that both the impurity-induced bond strengthening and the formation of zigzag bonds can lead to a significantly enhanced probability for chain formation in break junctions.