Tightness is a fundamental prerequisite to any underground storage. In storage salt caverns, a safe maximum admissible pressure must be selected to avoid product loss. The tensile strength of salt is small, and cavern pressure must be kept lower than geostatic pressure or, more precisely, lower than the least compressive stress at the cavern wall. The vertical stress can be assessed through density logs. The redistribution of stresses in the rock mass, due to the visco-plastic nature of rock salt, must be taken into account. A couple of cases in which a hydraulic connection between one cavern and another cavern, or between a cavern and the edge of a salt dome, are known. These connections originated in geological anomalies rather than in the creation of a fracture. There exists a pressure threshold, lower than the geostatic pressure, for which micro-fracturing and an increase in salt permeability occur, vindicating the position that a safety margin is needed when selecting the maximum pressure. Well tightness is important as well; it depends on several factors, among which are the quality of the cement, and the maximum fluid pressure in the cavern and along the access well. A tightness test is mandatory. The Nitrogen Leak Test is the most common such test. A review of selected gas-storage sites shows that, in most cases, the maximum admissible gradient at the casing shoe is 0.018 MPa/m (0.8 psi/ft), and up to 0.019 MPa/m (0.85 psi/ft) in some American states, values that are consistent with the considerations listed above.