An examination is made of stratospheric climate, circulation, and variability in configurations of the Hadley Centre Global Environmental Model version 2 (HadGEM2) differing only in stratospheric resolution and the placement of the model lid. This is made in the context of historical reconstructions of twentieth-century climate. A reduction in the westerly bias in the Northern Hemisphere polar night jet is found in the high-top model. The authors also find significant differences in the expression of tropical stratospheric variability, finding improvements in the high-top model for the presence of the quasi-biennial oscillation, for tropical upwelling consistent with interim European Centre for Medium-Range Weather Forecasts (ECMWF) Re-Analysis (ERA-Interim) data, and for interannual changes in stratospheric water vapor concentration comparable to satellite observations. Further differences are seen at high latitudes during winter in the frequency of occurrence of sudden stratospheric warmings (SSWs). The occurrence rate of SSWs in the high-top simulations, (7.2 ± 0.5) decade−1, is statistically consistent with observations, (6.0 ± 1.0) decade−1, whereas they are one-third as frequent in the low-top simulations, (2.5 ± 0.5) decade−1. Furthermore, the structure of the timing of winter final warmings is only captured in the high-top model. A similar characterization for the time evolution of the width of the tropical upper troposphere is found between model configurations. It is concluded that an adequate representation of the stratosphere is required to capture the important modes of tropical and extratropical stratospheric variability in models.