The present invention relates to a drainage device comprising:an internal chamberat least one inlet port and at least one outlet port communicating with the internal chambera shutter disposed at least in part in the internal chamberat least one first valve seat associated with the inlet port, the shutter being capable of bearing against the first seat in order to isolate the inlet port from the outlet port, in particular when the pressure difference between the inlet and outlet ports is less than a predetermined first opening pressure andat least one flow constriction associated with the outlet port, the shutter being capable of shutting said constriction, while allowing a minimum, safety flow to pass at a rate that is greater than or equal to 2.5 mL/h even in a maximally-shut position, referred to as a “closed” position, which position is reached in particular for pressure differences between the inlet and outlet ports that are greater than or equal to a predetermined closure pressure.