A cooled component, such as a turbine blade for gas turbines is provided, having efficient internal cooling, with an interior cooling passageway having a round cross-section. A row of feeding holes for the coolant are arranged spaced from each other in the direction of the longitudinal axis of the cooling passageway and originating from a common coolant channel. Each of the feeding holes intersects the cooling passageway tangentially. The ease of manufacturing the cooling component is improved in that the majority of the feeding holes have a hole diameter that is smaller than half of the hydraulic diameter of the cooling passageway, and selected feeding holes have a hole diameter that is greater than half of the hydraulic diameter of the cooling channel.