The CGILS (CFMIP-GASS Intercomparison of LES and SCMs) initiative brings together large-eddy simulations (LES) and single-column models to investigate and compare cloud feedbacks under idealized conditions. The first phase applied a surface warming of 2K for each of three cloud regimes: coastal stratus, decoupled stratocumulus, and shallow cumulus. The regimes cover the transition from overcast conditions near subtropical west coasts to the broken, fair-weather trade-wind conditions through the subtropical stratocumulus decks. The LES results generally support a positive cloud feedback in cumulus and stratocumulus conditions and negative feedback for coastal stratus. The SCMs, on the other hand, showed both positive and negative responses in all regimes, controlled by subtle balances among processes within each model's parameterized physics. Here we present the SCM results from the second phase of CGILS, which investigates the cloud response to a change in atmospheric carbon dioxide (in the absence of surface warming) as a parallel to similar experiments with global models in CMIP5. The LES results have been previously reported, and are largely consistent across models, showing a lower inversion and less cloud in all regimes. In the SCMs, a robust decrease in cloud cover is found for the coastal stratus regime, in agreement with the LES results. As was the case for the warming experiments, however, the SCMs show more diversity than the LES in the other regimes, exhibiting both positive and negative cloud responses. We present these results along with additional sensitivity experiments with the SCMs that remove cloud radiative effects or turn off parameterized convection help to understand the mechanisms controlling the different cloud responses.