Ocean-color remote sensing from space is currently limited to cloud-free areas. Consequently, the daily ocean coverage is 15-20%, and weekly products show no information in many areas. This limits considerably the utility of satellite ocean color observations for operational oceanography. Global coverage is required every three to five days in the open ocean and at least every day in the coastal zone. In view of the requirements for spatial coverage, and of the effects of clouds on observations of ocean color, an algorithm is proposed to estimate marine reflectance in the presence of a thin or broken cloud layer. The algorithm's theoretical basis is that cloud reflectance at some near-infrared wavelength may be accurately extrapolated to shorter wavelengths, whatever the cloud geometry, without any additional information. The interaction between cloud droplets and molecules, in particular, follows a λ-4 law. On the contrary, estimating aerosol scattering requires at least a measurement of its spectral dependence. Applying the algorithm to actual satellite ocean color imagery, a substantial gain in ocean coverage is obtained. The oceanic features retrieved below the clouds exhibit continuity with the adjacent features in clear areas. The daily ocean coverage is expected to be increased to up to 50% with the proposed algorithm, allowing one to resolve better phytoplankton blooms in the open ocean and "events" linked to wind forcing in the coastal zone. This could lead to important new information about the temporal variability of biological processes.