A normally closed valve that may be opened upon insertion of a nozzle permits two-way flow when opened by a luer-taper nozzle. The valve also is able to resist large back pressures. The valve includes a substantially rigid housing that defines a passageway having an inlet section and an outlet section. The housing has an exterior inlet face to which the inlet section opens. The inlet section preferably has tapered and expanding zones. The tapered zone is adjacent to the exterior inlet face and is shaped to receive the nozzle. The expanding zone is adjacent to the tapered zone and has a larger inner diameter than the tapered zone's inner diameter. The exterior of the inlet section of the housing may have threads to accept luer-lock threads that may surround the nozzle.