A methodology is proposed to correct satellite ocean-color imagery for the perturbing effects of the atmosphere and surface progressively, starting from the near infrared and advancing to the visible. First, a set of spectral bands is selected in the near infrared, for which the water body can be considered black, except in one of the spectral bands. The top-of-atmosphere reflectance in the selected bands, after correction for molecular scattering and sun glint contributions, is linearly combined to retrieve the ocean signal in the spectral band where the water body is not black. The coefficients of the linear combination minimize the perturbing effects, which are due to scattering and absorption by aerosols, and reflection by the surface. These effects are decomposed into principal components in the modeling. Second, other sets of spectral bands are selected, that progressively include shorter wavelengths. At each step, only the marine signal in one spectral band is unknown and therefore estimated. The methodology is developed for the Sea-viewing Wide Field-of-view Sensor (SeaWiFS), but is generally applicable to ocean-color sensors that measure in the visible and near infrared. Without measurements above one micrometer, however, the atmospheric correction is only accurate over Case-1 waters. Theoretical performance is evaluated from radiation-transfer simulations for a wide range of geophysical and angular conditions, including absorbing aerosols. Only Case-1 waters are considered in the simulations. The perturbing influence of the atmosphere and surface is minimized adequately for each set of wavelengths, except when the aerosol loading is large. The residual effects in the linear combination exhibit a bias of magnitude increasing with aerosol optical thickness. The bias can be reduced globally, by taking into account all the eigenvectors of the decomposition in principal components, not only the most significant ones. Errors in the estimated marine signal increase with decreasing wavelength (the residual effects at longer wavelengths propagate) and with increasing aerosol optical thickness. They become unacceptable when the aerosol optical thickness at 550 nm is above 0.3. Performance can be improved by optimizing the sets of selected wavelengths, or by using aerosol optical thickness estimated from the satellite data.