Appliances for cooking food under pressure are disclosed herein. In one embodiment, an appliance comprises a vessel and a lid fitted and locked on the vessel in order to form a leaktight cooking enclosure. The appliance further comprises at least one jaw for locking the lid relative to the vessel and a device for driving the at least one jaw between a locking position and an unlocking position. The appliance also includes a module for fitting on and releasably securing to the lid. The module includes at least a device for controlling locking and unlocking of the lid relative to the vessel. Also disclosed are other alternatives applicable to domestic appliances for cooking food under pressure.