A variable displacement vane-type fluid pump is provided which permits improved regulation of the pump discharge such that the pump can meet the various requirements of lubrication for internal combustion engines at all speeds with minimized use of power. Of course, the vane pump may also be utilized in a wide range of power transmission and other fluid distribution applications. The vane pump of the invention may also use both hydrostatic and mechanical actuators to control the position of its containment ring or eccentric ring and hence, regulate the output of the pump. According to yet another aspect of the present invention, to prevent inlet flow restriction or cavitation, a valve may be provided to permit some of the pump outlet or discharge flow to bleed into the pump inlet to provide needed velocity energy to the fluid flow into the pump inlet. A system for lubrication of an engine using a fixed displacement pump for providing an engine speed input for controlling a second main variable displacement type oil pump and maintaining a target oil pressure in the oil pressure circuit. A solenoid valve is used for venting output of the fixed displacement pump to create a second target oil pressure characteristic or curve when desired.