A component is repaired by removing a damaged region to form a cavity, in which layered repair inserts are installed. The profile of the cavity, and of the exposed surface of each repair insert is measured to serve as the basis for the contact surface of each subsequent repair insert. The repair inserts are fused to the wall of the cavity and to each other in a process in which heated locations of each repair insert are successively heated to minimize heat transfer within the repair inserts and in the underlying substrate material. The repair inserts may be made in a powder bed process from an alloy powder having the same composition as the material of the substrate.