A gas turbine transition piece adapted to carry combustion gases in a hot gas path extending between a gas turbine combustion chamber and a first stage of the gas turbine, includes a hollow duct having a forward end adapted for connection to a combustor liner and an aft end adapted for connection to a first stage nozzle. One or more dilution air holes are located proximate the forward end, the dilution holes each fitted with a hollow sleeve penetrating into the hot gas path within the hollow duct, the hollow sleeves adapted to supply cooling air into the hot gas path.