A component of a turbine stage of a gas turbine engine is provided, the component forming an endwall for the working gas annulus of the stage. The component has one or more internal plena behind the endwall which, in use, contain a flow of cooling air. The component further has a plurality of exhaust holes in the endwall. The holes connect the plena to a gas-washed surface of the endwall such that the cooling air effuses through the holes to form a cooling film over the gas-washed surface. Each exhaust hole has a flow cross-sectional area which is greater at an intermediate position between the entrance of the hole from the respective plenum and the exit of the hole to the gas-washed surface than it is at said exit.