An inflatable structure may be formed from a single piece of flexible film. The inflatable structure may include quilting seals which divide the inflatable chamber. The inflatable structure may include a one-way valve including an internal valve opening, a channel, and an external valve opening. A locator aperture positioned in the channel may be surrounded by a valve position-retention seal. A corresponding inflation device fills the inflatable structure with air and may do so without requiring heat sealing or insertion into the one-way valve. The inflation device may include a mechanical registration device configured to engage the locator aperture and position the one-way valve at a desired position with respect to an outlet of a source of pressurized air. The inflation device may detect when the inflatable structure is filled with a desired amount of air and automatically shut off the source of pressurized air.