Climate sensitivity in Earth System Models (ESMs) is an emergent property that is affected by structural (missing or inaccurate model physics) and parametric (variations in model parameters) uncertainty. This work provides the first quantitative assessment of the role of compensation between uncertainties in aerosol forcing and atmospheric parameters, and their impact on the climate sensitivity of the Community Atmosphere Model, Version 4 (CAM4). Running the model with prescribed ocean and ice conditions, we perturb four parameters related to sulfate and black carbon aerosol radiative forcing and distribution, as well as five atmospheric parameters related to clouds, convection, and radiative flux. The atmospheric parameters explain more than 85 % of the variance in climate sensitivity for the ranges of parameters explored here, with two parameters being the most important: one controlling low cloud amount, and one controlling the timescale for deep convection. Although the aerosol parameters strongly affect aerosol optical depth, the effects of these aerosol parameters on climate sensitivity are substantially weaker than the effects of the atmospheric parameters. Based on comparisons to inter-model spread of other ESMs, we conclude that structural uncertainties in this configuration of CAM4 likely contribute three times more to uncertainty in climate sensitivity than parametric uncertainty. We provide several parameter sets that could provide plausible (measured by a skill score) configurations of CAM4, but with different sulfate aerosol radiative forcing, black carbon radiative forcing, and climate sensitivity.