A solenoid operated valve includes a valve block defining a valve lumen, a poppet slidably disposed within the valve lumen, a solenoid including an annular winding with an internal surface defining a winding lumen and an external surface, and a core including a central core portion disposed within the winding lumen and an annular core portion disposed outside the external surface of the winding, and an armature including a central armature portion disposed within the winding lumen and an annular armature portion disposed outside the external surface of the winding, wherein the armature is in communication with the poppet so that movement of one is translated into movement of the other. Solenoids for such valves are provided. Also provided are methods of assembling solenoid valves.