A method for depressurizing a vehicular fuel storage system including a first portion and a second portion, the first portion being in fluid communication with a closable filler head opening, the first portion being separated from the second portion by a valve, the method including: in a first time period, depressurizing the first portion by bringing the first portion in communication with the atmosphere, while the valve and the filler head opening are closed; in a second time period, depressurizing the second portion by bringing the second portion in communication with the atmosphere; and obtaining readiness for access to the filler head opening as from the end of the first time period.