Laser entrance hole (LEH) windows for hohlraums must have minimal thickness yet must contain low-temperature tamping gas in a reproducible envelope at 52 kPa. Given the high cost of a window failure, it is important to understand variability in the finished windows. Polyimide LEH window pressure deflection profiles were measured at 18 K. The shape and magnitude of pressure deflections of LEH windows were well described using thin film elastic mechanics. Subsequently, 24 windows with 3.9-mm apertures were selected from several production lots to measure reproducibility. The windows were cooled to 18 K, and their leak rates, deflections to 52 kPa, and burst pressures were measured. The mean window deflection at 18 K was 260 m, with a standard deviation of 20 m. Variability in window deflections was well described by an anisotropic initial strain model. Window burst pressure was found to obey first-order Weibull statistics. The predicted failure rate for the use conditions was extrapolated to be <0.1%.