A cryogenic storage tank comprises a partition that divides a cryogen space into a main storage space and an auxiliary space. A valve disposed inside the cryogen space is associated with a first fluid passage through the partition. The valve comprises a valve member that is actuatable by fluid forces within the cryogen space. A second fluid passage through the partition comprises a restricted flow area that is dimensioned to have a cross-sectional flow area that is smaller than that of a fill conduit such that there is a detectable increase in back-pressure when the main storage space is filled with liquefied gas. A preferred method comprises establishing a vapor-filled ullage space when the main storage space is being vented and re-filled with cryogenic fluid, by draining liquefied gas from the auxiliary space through the first fluid passage under the influence of a vapor pressure differential permitted by the partition. If the vapor pressure differential reverses during re-filling, the valve can close to preserve the vapor-filled ullage volume. Re-filling is stopped when an increase in back pressure is detected during re-filling.