Aerosol radiative forcing uncertainty affects estimates of climate sensitivity and limits model skill in terms of making climate projections. Efforts to improve the representations of physical processes in climate models, including extensive comparisons with observations, have not significantly constrained the range of possible aerosol forcing values. A far stronger constraint, in particular for the lower (most-negative) bound, can be achieved using global mean energy balance arguments based on observed changes in historical temperature. Here, we show that structural deficiencies in a climate model, revealed as inconsistencies among observationally constrained cloud properties in the model, limit the effectiveness of observational constraint of the uncertain physical processes. We sample the uncertainty in 37 model parameters related to aerosols, clouds, and radiation in a perturbed parameter ensemble of the UK Earth System Model and evaluate 1 million model variants (different parameter settings from Gaussian process emulators) against satellite-derived observations over several cloudy regions. Our analysis of a very large set of model variants exposes model internal inconsistencies that would not be apparent in a small set of model simulations, of an order that may be evaluated during model-tuning efforts. Incorporating observations associated with these inconsistencies weakens any forcing constraint because they require a wider range of parameter values to accommodate conflicting information. We show that, by neglecting variables associated with these inconsistencies, it is possible to reduce the parametric uncertainty in global mean aerosol forcing by more than 50 %, constraining it to a range (around −1.3 to −0.1 W m−2) in close agreement with energy balance constraints. Our estimated aerosol forcing range is the maximum feasible constraint using our structurally imperfect model and the chosen observations. Structural model developments targeted at the identified inconsistencies would enable a larger set of observations to be used for constraint, which would then very likely narrow the uncertainty further and possibly alter the central estimate. Such an approach provides a rigorous pathway to improved model realism and reduced uncertainty that has so far not been achieved through the normal model development approach.