Thin polyimide (PI) windows are used to contain gases in a variety of targets including National Ignition Facility ignition targets. Magnetized liner inertial fusion targets shot on the Sandia National Laboratory Z-facility and on the University of Rochester OMEGA laser facility typically contain deuterium gas in the pressure range from a few to as many as 15 atm, with the window diameters ranging from a few tenths of a millimeter at OMEGA to several millimeters at the Z-facility. These pressures are generally higher, with larger plastic deformations, than previously investigated. We have fabricated and assembled PI windows and measured their deflections and burst pressures for these pressure and diameter ranges at room temperature. The results are dependent on PI formulation and the details of the window assembly geometry. We analyze the scaling behavior of these higher-pressure windows similarly to but with an extension of the analysis of Bhandarkar et al. [Fusion Sci. Technol., Vol. 70, p. 332] and show that predictions of pressure-induced deflection using this analysis applies to a more complex window geometry than previously reported.