A poppet valve assembly includes a body and first and second check valves. The body includes opposing first and second axial end portions. The first end portion has a first circumferential surface, a first end surface, and a tapered surface, which seals with a main valve seat. The second axial end portion defines at least one metering slot. The body defines first and second internal passages. The first internal passage includes an opening in the first end surface, is in fluid communication with one of the metering slots, and has a first check valve seat. The second internal passage includes an opening in the first circumferential surface, is in fluid communication with one of the metering slot, and has a second check valve seat. The first and second check valves are disposed in the respective internal passages and are adapted for sealing engagement with the respective check valve seats.