A cooking appliance for cooking food under pressure, the appliance comprising at least: - a circular vessel and a circular lid for placing to bear on the vessel in order to form a cooking enclosure that is made substantially leaktight with the help of sealing means interposed between the vessel and the lid, - locking means arranged on the vessel and the lid and forming vessel ramps and lid ramps that are for co-operating together by the vessel and the lid turning relative to each other so that the lid ramps come under the vessel ramps in order to lock the lid on the vessel, - the vessel being defined by a top edge from which there extends the wall of the vessel, and the vessel ramps are arranged under said top edge starting from a distance "d1" from said top edge, - the lid is defined by an outer bearing edge followed by a cylindrical belt of size matching the size of the vessel so as to be capable of coming into fitted contact with the wall of the vessel when the lid is put into place bearing in or on the vessel via its outer bearing edge, the lid ramps being arranged on said cylindrical belt at a distance "d2" from the outer bearing edge, the distances d1 and d2 being such as to enable the vessel ramps and the lid ramps to co-operate together when the lid is put into place bearing against the vessel, the lid ramps being for passing under the vessel ramps in order to bear in sliding manner against the vessel ramps when the lid is caused to turn relative to the vessel inside the vessel so as to ensure locking, said appliance being characterized in that: - the outer bearing edge is continued by a reentrant portion forming the cylindrical belt, said reentrant portion being of a size that matches the size of the vessel, but smaller, so as to be capable of being inserted inside the vessel so that the reentrant portion comes into fitted contact when the lid is put into place. - a circular vessel and a circular lid for placing to bear on the vessel in order to form a cooking enclosure that is made substantially leaktight with the help of sealing means interposed between the vessel and the lid, - locking means arranged on the vessel and the lid and forming vessel ramps and lid ramps that are for co-operating together by the vessel and the lid turning relative to each other so that the lid ramps come under the vessel ramps in order to lock the lid on the vessel, - the vessel being defined by a top edge from which there extends the wall of the vessel, and the vessel ramps are arranged under said top edge starting from a distance "d1" from said top edge, - the lid is defined by an outer bearing edge followed by a cylindrical belt of size matching the size of the vessel so as to be capable of coming into fitted contact with the wall of the vessel when the lid is put into place bearing in or on the vessel via its outer bearing edge, the lid ramps being arranged on said cylindrical belt at a distance "d2" from the outer bearing edge, the distances d1 and d2 being such as to enable the vessel ramps and the lid ramps to co-operate together when the lid is put into place bearing against the vessel, the lid ramps being for passing under the vessel ramps in order to bear in sliding manner against the vessel ramps when the lid is caused to turn relative to the vessel inside the vessel so as to ensure locking, said appliance being characterized in that: - the outer bearing edge is continued by a reentrant portion forming the cylindrical belt, said reentrant portion being of a size that matches the size of the vessel, but smaller, so as to be capable of being inserted inside the vessel so that the reentrant portion comes into fitted contact when the lid is put into place. - the outer bearing edge is continued by a reentrant portion forming the cylindrical belt, said reentrant portion being of a size that matches the size of the vessel, but smaller, so as to be capable of being inserted inside the vessel so that the reentrant portion comes into fitted contact when the lid is put into place.