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Recent studies have shown that, in response to a surface warming, the marine tropical low-cloud cover (LCC) as observed by passive-sensor satellites substantially decreases, therefore generating a smaller negative value of the top-of-the-atmosphere (TOA) cloud radiative effect (CRE). Here we study the LCC and CRE interannual changes in response to sea surface temperature (SST) forcings in the GISS model E2 climate model, a developmental version of the GISS model E3 climate model, and in 12 other climate models, as a function of their ability to represent the vertical structure of the cloud response to SST change against 10 years of CALIPSO (Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observations) observations. The more realistic models (those that satisfy the observational constraint) capture the observed interannual LCC change quite well (1LCC/1SST = −3.49 ± 1.01 % K−1 vs. 1LCC/1SSTobs = −3.59 ± 0.28 % K−1 ) while the others largely underestimate it (1LCC/1SST = −1.32 ± 1.28 % K−1 ). Consequently, the more realistic models simulate more positive shortwave (SW) feedback (1CRE/1SST = 2.60 ± 1.13 W m−2 K−1 ) than the less realistic models (1CRE/1SST = 0.87 ± 2.63 W m−2 K−1 ), in better agreement with the observations (1CRE/1SSTobs = 3 ± 0.26 W m−2 K−1 ), although slightly underestimated. The ability of the models to represent moist processes within the planetary boundary layer (PBL) and produce persistent stratocumulus (Sc) decks appears crucial to replicating the observed relationship between clouds, radiation and surface temperature. This relationship is different depending on the type of low clouds in the observations. Over stratocumulus regions, cloud-top height increases slightly with SST, accompanied by a large decrease in cloud fraction, whereas over trade cumulus (Cu) regions, cloud fraction decreases everywhere, to a smaller extent.