A shock absorber for a vehicle includes a pressure tube that defines a fluid chamber. A piston disposed within the fluid chamber divides the fluid chamber into an upper working chamber and a lower working chamber. The piston defines a compression passage and a rebound passage which extend through the piston between the upper working chamber and the lower working chamber. A valve disc assembly engages the piston and controls the flow of fluid between the upper working chamber and the lower working chamber. The valve disc assembly includes a bleed disc that defines an orifice with a substantially non-linear contour. The orifice extends to an outer diameter of the bleed disc, and forms a bleed channel between the upper working chamber and the lower working chamber.