Indirect-drive ignition targets require that the hohlraums contain a gas of helium, hydrogen, or a mixture of the two. For this purpose, thin polyimide windows must cover the laser entrance holes and any other hohlraum ports. We have fabricated, assembled, and tested such windows and have measured their deflection as a function of applied pressure. We also measured the permeation of helium through them. We find that the deflection is approximately linear with pressure and that the two polyimide formulations that we tested are internally consistent as well as consistent with the earlier data of Powell and Lopez when scaled for geometry. We also find that the permeation is linear with pressure, despite the large increase in window area-to-thickness ratio that occurs during a measurement run that results from the window deflection and thinning as the pressure increases. The permeability of our spin-cast material is 0.65 × 10-13 sccs/cmPa, with an uncertainty of 15% (sccs = standard cubic centimeters per second).