We compare atmospheric temperature changes in satellite data and in model ensembles performed under phases 5 and 6 of the Coupled Model Intercomparison Project (CMIP5 and CMIP6). In the lower stratosphere, multidecadal stratospheric cooling during the period of strong ozone depletion is smaller in newer CMIP6 simulations than in CMIP5 or satellite data. In the troposphere, however, despite forcing and climate sensitivity differences between the two CMIP ensembles, their ensemble-average global warming over 1979–2019 is very similar. We also examine four properties of tropical behavior governed by basic physical processes. The first three are ratios between trends in water vapor (WV) and trends in sea surface temperature (SST), lower-tropospheric temperature (TLT), and mid- to upper-tropospheric temperature (TMT). The fourth property is the ratio between TMT and SST trends. All four ratios are tightly constrained in CMIP simulations but diverge markedly in observations. Model trend ratios between WV and temperature are closest to observed ratios when the latter are calculated with datasets exhibiting larger tropical warming of the ocean surface and troposphere. For the TMT/SST ratio, model–data consistency depends on the combination of observations used to estimate TMT and SST trends. If model expectations of these four covariance relationships are realistic, our findings reflect either a systematic low bias in satellite tropospheric temperature trends or an overestimate of the observed atmospheric moistening signal. It is currently difficult to determine which interpretation is more credible. Nevertheless, our analysis reveals anomalous covariance behavior in several observational datasets and illustrates the diagnostic power of simultaneously considering multiple complementary variables.