Low clouds over tropical oceans reflect a great proportion of solar radiation back to space and thereby cool the Earth, yet this phenomenon has been poorly simulated in several previous generations of climate models. The principal aim of the present study is to employ satellite observations to evaluate the representation of marine tropical low clouds and their radiative effect at the top of the atmosphere in a subset of latest climate models participating in CMIP6. We strive for regime-oriented model validation and hence introduce a qualitative approach to discriminate stratocumulus (Sc) from shallow cumulus (Cu). The novel Sc-Cu categorization has a conceptual advantage of being based on cloud properties, rather than relying on a model response to a cloud-controlling factor. We find that CMIP6 models underestimate low-cloud cover in both Sc- and Cu-regions of tropical oceans. A more detailed investigation of cloud biases reveals that most CMIP6 models underestimate the relative frequency of occurrence (RFO) of Sc and overestimate RFO of Cu. We further demonstrate that tropical low cloudiness in CMIP6 models remains too bright. The regime-oriented validation represents the basis for improving parameterizations of physical processes that determine the cloud cover and radiative impact of Sc and Cu, which are still misrepresented in current climate models.