A hydraulic damper assembly comprises a main tube defining a fluid chamber. An external tube extends about the main tube defining a compensation chamber between the main and external tubes. A main piston, located in the main tube, divides the fluid chamber into a compression chamber and a rebound chamber. A piston rod couples to the main piston. A base valve, located in the compression chamber, couples to the main tube. A hydraulic compression stop, located in the compression chamber, includes an additional piston, an insert, and a fixing member. The additional piston couples to the main piston. The insert, located in the compression chamber, couples to the base valve. The insert has a main section and a terminal section. The terminal section having an external diameter that is less than an external diameter of the main section.