There is provided a method of making a composite hat stiffener. The method has the steps of curing a composite hat stiffener in a hat tool to form a pre-cured composite hat stiffener. The pre-cured composite hat stiffener has a composite hat section, a plurality of composite stiffening plies with a body ply, a wrap ply, and a base ply, all coupled to the composite hat section, wherein the body ply is coupled to a first side of the composite hat section, the wrap ply is coupled to the body ply, and the base ply is coupled to the body ply and the wrap ply, a pair of radius filler noodles coupled to the composite hat section and disposed between the plurality of composite stiffening plies, and an outer ply coupled to the composite hat section. The method further includes bonding the pre-cured composite hat stiffener to a structure surface.