Previous generations of climate models have been shown to under-estimate the occurrence of tropical low-level clouds and to over-estimate their radiative effects. This study analyzes outputs from multiple climate models participating in the Fifth phase of the Coupled Model Intercomparison Project (CMIP5) using the Cloud Feedback Model Intercomparison Project Observations Simulator Package (COSP), and compares them with different satellite data sets. Those include CALIPSO lidar observations, PARASOL mono-directional reflectances and CERES radiative fluxes at the top of the atmosphere. We show that current state-of-the-art climate models predict overly bright low-clouds, even for a correct low-cloud cover. The impact of these biases on the Earth' radiation budget, however, is reduced by compensating errors. Those include the tendency of models to under-estimate the low-cloud cover and to over-estimate the occurrence of mid- and high-clouds above low-clouds. Finally, we show that models poorly represent the dependence of the vertical structure of low-clouds on large-scale environmental conditions. The implications of this ‘too few, too bright low-cloud problem’ for climate sensitivity and model development are discussed.