Some modifications that could be made, separately or together, have been conceived as improvements of the generic design of a structure of the type described in “Hybrid Inflatable Pressure Vessel” (MSC-23024/92), NASA Tech Briefs, Vol. 28, No. 4 (April 2004), page 44. To recapitulate: The vessel is a hybrid that comprises an inflatable shell attached to a rigid structure. The inflatable shell is, itself, a hybrid that comprises (1) a pressure bladder restrained against expansion by (2) a restraint layer that comprises a web of straps made from high-strength polymeric fabrics. The present improvements are intended to overcome deficiencies in those aspects of the original design that pertain to attachment of the inflatable shell to the rigid structure. In a typical intended application, such attachment(s) would be made at one or more window or hatch frames to incorporate the windows or hatches as integral parts of the overall vessel.