There is provided a composite hat stiffener, a composite hat-stiffened pressure web, and a method of making the same. The composite hat stiffener has a composite hat section having a first side and a second side. The composite hat stiffener further has a plurality of composite stiffening plies coupled to the composite hat section. The plurality of composite stiffening plies include a body ply coupled to the first side of the composite hat section, a wrap ply coupled the body ply, and a base ply coupled to the body ply and the wrap ply. The composite hat stiffener further has a pair of radius filler noodles coupled to the composite hat section and disposed between the plurality of composite stiffening plies. The composite hat stiffener further has an outer ply coupled to the second side of the composite hat section.