In certain critical applications it is current practice to incorporate sealed electron devices within an outer hermetic enclosure for increased seal assurance. An exact solution is now given for the gas influx into such a doubled hermetic enclosure when each enclosure has a given leak size. This solution allows a comparison to be made between the leakage into a single isolated semiconductor package and that into the same package when it is protected by an outer enclosure. If the leaks are in the molecular flow regime, solutions for the pressure within the enclosures are of the form

for i = 1,2, where P
bis the external applied pressure at t > 0 and

,

are constants whose values depend only on the ratios of leak rates and of volumes. The general behavior is described in terms of a merit factor as a measure of the hermetic improvement for doubled enclosures over that of a single enclosure, and characteristics are derived for a broad spectrum of system dimensions. It is shown that a significant improvement in hermeticity over a long time span is not an apriori result of using an outer enclosure.