<p>The sixth Coupled Model Intercomparison Project (CMIP6) constitutes the latest update on expected future climate change based on a new generation of climate models. To extract reliable estimates of future warming and related uncertainties from these models, the spread in their projections is often translated into probabilistic estimates such as mean and likely range. Here, we use a model weighting approach, which accounts for a model's historical performance based on several diagnostics as well as possible model inter-dependence within the CMIP6 ensemble, to calculate constrained distributions of global mean temperature change. We investigate the skill of our approach in a perfect model test, where we remove each CMIP6 model from the ensemble in turn, use it as pseudo-observation in the historical period, and evaluate the weighted CMIP6 ensemble against it in the future. This is complemented by a second perfect model test drawing on the previous-generation CMIP5 models as pseudo-observations. In addition, we show that our independence diagnostics correctly clusters models known to be similar based on a CMIP6 <q>family tree</q>, which enables applying a weighting based on the degree of inter-model dependence. We then apply the weighting approach, based on two observational estimates (ERA5 and MERRA2), to constrain CMIP6 projections in weak (SSP1-2.6) and strong (SSP5-8.5) climate change scenarios. Our results show a reduction in projected mean warming for both scenarios because some CMIP6 models with high future warming receive systematically lower performance weights. The mean of end-of-century warming (2081–2100 relative to 1995–2014) for SSP5-8.5 with weighting is 3.7 °C, compared to 4.1 °C without weighting; the likely (66 %) uncertainty range is 3.1 °C to 4.6 °C, a decrease of 13 %. For SSP1-2.6, weighted end-of-century warming is 1 °C (0.7 °C to 1.4 °C). Applying the weighting to estimates of Transient Climate Response (TCR) yields 1.9 °C (1.6 °C to 2.1 °C – a reduction in the likely uncertainty range of 46 %), which is consistent with estimates from previous model generations and other lines of evidence.</p>