A pressure in a compression chamber of direct injection fuel pump is regulated to a single pressure during a direct injection fuel pump compression stroke while pressure is greater than an output pressure of a low pressure pump supplying fuel to the direct injection fuel pump. The outlet pressure of the direct injection fuel pump is maintained at a pressure during the direct injection fuel pump compression stroke. The fuel flow from the direct injection fuel pump to an engine is ceased during the direct injection fuel pump compression stroke. An independent claim is included for direct injection fuel pump.