A vehicular hydraulic system with a pump and first and second hydraulic applications arranged in series. The fluid upstream of the first application may be elevated to a first threshold pressure value. A pressure-dump valve is disposed downstream of the first application and fluid entering the valve flows through an inlet port, primary flow channel and outlet port of the valve to the second hydraulic application. The valve includes a valve member that axially slides within an elongate valve chamber, partitioning the primary flow channel from a low pressure volume. The valve also includes a low pressure port and a bypass port that diverts fluid past the second application. The valve member is biased into a position wherein fluid is diverted through the bypass port when the pressure in the primary flow channel exceeds a second threshold value. The first threshold value is greater than the second threshold value.