Abstract: A hydraulic system is disclosed for use with a machine. The hydraulic system may have a tank, a motor with a fluid inlet and a fluid outlet, and a pump configured to draw fluid from the tank and discharge the fluid at elevated pressures to the motor. An output of the pump is adjustable to regulate a speed of the motor. The hydraulic system may also have a low-speed valve located between the fluid outlet of the motor and the tank. The low-speed valve may be configured to reduce a positive speed of the motor below a lowest positive speed attainable through control of pump output.