A cuff pressure stabilizer includes a substantially rigid protective housing and a balloon disposed therein. The balloon has a base low pressure of 10 cm H2O when it contains a base low-pressure volume of air. When the balloon contains a first medium-pressure volume of air, the balloon has a first medium pressure of 25 cm H2O. When the balloon contains a second medium-pressure volume of air, the balloon has a second medium pressure of 40 cm H2O, and at least 20% of an outer surface of the balloon touches a portion of the inner surface of the housing. The second medium-pressure volume of air equals the base low-pressure volume of air plus a second incremental quantity of air that is less than 60 cc. Other embodiments are also described.