A laryngeal mask airway (LMA) device includes a backplate, an inflatable balloon, an airway tube, and a non-inflatable skeleton, which extends anteriorly from the backplate, and which is shaped so as to define a skeleton anterior side that has a pre-formed shape. A distal end of an inflation tube is coupled in fluid communication with (i) an interior of the inflatable balloon for supplying air to the inflatable balloon, and (ii) at least a portion of the skeleton anterior side. The inflatable balloon is shaped so as to define an inflatable annular cuff which (a) covers at least a portion of the skeleton anterior side, and (b) has a cuff anterior side that is configured to form a seal around a laryngeal inlet of a patient when the inflatable annular cuff is disposed at an LMA-insertion location within a throat of the patient. Other embodiments are also described.