During the early to mid-Holocene vegetation expanded to cover much of the present-day Sahara. Although driven by a well-understood difference in the orbital configuration, general circulation models have generally failed to simulate the required rainfall increase. One possible explanation is the presence of systematic biases in the representations of atmospheric convection which might also impact future projections. We employ a Bayesian method to learn from an ensemble of present day and mid-Holocene simulations that vary parameters in the convection, boundary layer and cloud schemes. The model can reproduce the ‘Green Sahara’ rainfall if mixing between convective plumes and the environment is increased in the upper troposphere relative to lower down. This does not appreciably impact the present day simulation, meaning that the palaeoclimate reconstructions are able to narrow constraints on suitable parameter ranges. This suggests that other uncertain components of climate models could be targeted in this way.