Abstract: An inflatable packer used in a well and having a mandrel carrying upper and lower heads, a normally retracted inflatable packer element including an inner elastomer bladder and an outer expansible armor or carcass, the ends of the packer element being anchored to respective heads, and in one embodiment a hydraulically operable system that applies restraining force to the heads which controls the shape and deployment of the packer element during inflation and prevents entrapment of fluid bubbles outside the element and the formation of Z-folds in the bladder. In other embodiments the restraining force is supplied by a stack of disc springs, by frictional engagement between parts, by a shearing action of materials, by swaging a sleeve member, and by axially crushing a sleeve member.