A major source of uncertainty in the effective radiative forcing due to aerosol-cloud interactions (ERFaci) arises from parameters that represent unresolved sub-grid-scale processes in global climate models. Constraining parametric uncertainty requires identifying parameters driving the largest spread in ERFaci. Perturbed parameter ensembles (PPE) address this by systematically varying parameters related to aerosol emission, cloud microphysics, and associated small-scale processes. We perform a global sensitivity analysis of the three components of ERFaci from liquid clouds, the Twomey effect, liquid water path (LWP), and cloud fraction (CF) adjustments, in a PPE with and without constraining to the model's present-day base state. Under uniform prior sampling, autoconversion parameters unrelated to aerosol activation counterintuitively dominate the Twomey effect. Only after constraining the base state are aerosol emission and activation parameters revealed as controlling parameters for the Twomey effect. The apparent control of autoconversion parameters over the Twomey effect arises because these parameters control the cloud base state, which in turn affects the strength of the Twomey effect. The dominant parameters for LWP and CF adjustments remain related to autoconversion before and after the constraint. Constraining to the base state is therefore essential to inferring the correct parameters and processes controlling the model’s climate responses.