An example valve includes: (i) a valve body defining a longitudinal cavity, where the valve body includes a supply inlet and an operating outlet; (ii) a cage disposed in the longitudinal cavity, where the cage includes (a) a first opening fluidly coupled to the supply outlet, and (b) a second opening fluidly coupled to the operating outlet; and (iii) a spool mounted within the cage and configured to move axially therein. When the valve is actuated, the spool moves within the cage to form a gap, thereby allowing pressurized fluid to flow from the supply inlet through the first opening, the gap, and the second opening to the operating outlet. A flow area defined around an exterior peripheral surface of the spool changes upstream from the gap at a first rate, and changes downstream from the gap at a second rate that is different from the first rate.