A sealed and insulating reservoir contains a pressurized cold fluid in a rigid, sealed enclosure. A fluidtight membrane is positioned to contact the cold fluid contained in the reservoir. An insulating barrier is placed between the fluidtight membrane and the internal surface of the rigid enclosure, with the insulating barrier forming a support surface to support the fluidtight membrane. A pressure balancing device is able to limit the pressure difference between a first sealed volume located inside the fluidtight membrane, and a second sealed volume located outside the fluidtight membrane. The pressure balancing device typically includes a fluid circuit having two chambers sealingly separated by a movable separator. The first chamber is linked to the first sealed volume, and the second chamber is linked to the second sealed volume. The movable separator exerts a loading force in the direction of the second chamber.