A two-stage shock absorber has a pressure tube within which a piston assembly is slidably disposed. A piston rod is attached to the piston assembly and extends out of the pressure tube. A sleeve is slidably disposed within the pressure tube and engages the piston rod. After a specified amount of movement of the piston assembly with respect to the pressure tube in an extension movement of the shock absorber, the sleeve engages a plurality of spirally positioned bores on the piston rod and reduces the fluid flow through the valve assembly to progressively switch the shock absorber from soft damping to firm damping. In another embodiment the sleeve engages a spiral groove of variable depth on the piston rod to reduce the fluid flow through the valve assembly to progressively switch the shock absorber from soft damping to firm damping. In yet another embodiment of the present invention, the sleeve engages a tapered slot of variable cross-section to reduce the fluid flow through the valve assembly to progressively switch the shock absorber from soft damping to firm damping.