A variable-nozzle turbocharger includes a variable vane mechanism that has an annular nozzle ring supporting an array of rotatable vanes, an insert having a tubular portion sealingly received into a bore of the turbine housing and having a nozzle portion extending radially out from one end of the tubular portion and being axially spaced from the nozzle ring with the vanes therebetween, and a plurality of two-piece self-centering spacer assemblies connected between the nozzle portion of the insert and the nozzle ring. Each spacer assembly comprises a tubular sleeve and a separate pin that passes through the through-passage of the sleeve, end portions of the pin being secured respectively to the nozzle ring and the nozzle portion. One end of each sleeve has a conical surface and engages in a corresponding conical countersink in the adjacent face of the nozzle ring or nozzle portion.