The tendency of climate models to overstate warming in the tropical troposphere has long been noted. Here we examine individual runs from 38 newly-released Coupled Model Intercomparison Project version 6 (CMIP6) models and show that the warm bias is now observable globally as well. We compare CMIP6 runs against observational series drawn from satellites, weather balloons and reanalysis products. We focus on the 1979-2014 interval, the maximum span for which all observational products are available and for which models were run using historically-observed forcings. For lower- and mid-troposphere layers both globally and in the tropics, all 38 models overpredict warming in every target observational analogue, in most cases significantly so, and the average differences between models and observations are statistically significant. We present evidence that consistency with observed warming would require lower model Equilibrium Climate Sensitivity (ECS) values.