Half-Heusler alloys based on TiNiSn are promising thermoelectric materials characterised by large power factors, good mechanical and thermal stabilities; but they are limited by large thermal conductivities. A variety of strategies have been used to disrupt their thermal transport, including alloying with heavy, generally expensive, elements and nanostructuring, enabling figures of merit, ZT ≥ 1 at elevated temperatures (>773 K). Here, we demonstrate an alternative strategy that is based around the partial segregation of excess Cu leading to grain-by-grain compositional variations, the formation of extruded Cu ‘wetting’ layers between grains and – most importantly – the presence of statistically distributed interstitials that reduce the thermal conductivity effectively through point-defect scattering. Our best TiNiCuySn (y ≤ 0.1) compositions have a temperature-averaged ZTdevice = 0.3-0.4 and estimated leg power outputs of 6-7 W cm-2 in the 323-773 K temperature range. This is a significant development as these materials were prepared using a straightforward processing method, do not contain any toxic, expensive or scarce elements and are therefore promising candidates for large scale production.