A medical valve is provided that includes a housing having a main conduit and a branch extending from the main conduit and in fluid communication with it. The bore of the branch has an elastomeric septum piston disposed therewithin and at least a portion of the elastomeric septum piston is movable by either compression or by a longitudinal advancement along the secondary bore towards the bore of the main conduit. In one embodiment, the septum piston is cylindrical and includes a centrally positioned slit. The bore of the branch includes two opposing projecting members along a distal portion of the bore which effectively narrow the diameter of the bore. When the elastomeric member is pushed from a proximal position to a distal position, it is transversely compressed by the projecting members to open the slit and allow fluid passage. After removal of the longitudinal displacement force the septum piston retracts away from the distal portion back to the proximal portion.