Abstract. Aerosol radiative forcing uncertainty affects estimates of climate sensitivity and limits model skill at 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, limit the effectiveness of observational constraint of the uncertain physical processes. We sample uncertainty in 37 model parameters related to aerosols, clouds and radiation in a perturbed parameter ensemble of the UK Earth System Model and evaluate one million model variants (different parameter settings from Gaussian Process emulators) against satellite-derived observations over several cloudy regions. We show it is possible to reduce the parametric uncertainty in global mean aerosol forcing by more than 50 % to a range in close agreement with energy-balance constraints (around -1.3 to -0.1 W m-2). However, incorporating observations associated with model inconsistencies weakens the constraint because the inconsistencies introduce conflicting information about relationships between model parameter values and aerosol forcing. Our estimated aerosol forcing range is the maximum feasible constraint using these observations and our structurally imperfect model. Structural model developments, targeted at the inconsistencies identified here, would enable a larger set of observations to be used for constraint, which would then narrow the uncertainty further.