Many standard methods used for the remote sensing of ocean colour have been developed, though mainly for clean, open ocean waters. This means that they may not always be effective in complex waters potentially containing high concentrations of optically significant constituents. This paper presents new empirical formulas for estimating selected inherent optical properties of water from remote-sensing reflectance spectra (), derived, among other things, for waters with high concentrations of dissolved and suspended substances. These formulas include one for estimating the backscattering coefficient (620) directly from the magnitude of in the red part of the spectrum, and another for estimating the absorption coefficient (440) from the hue angle . The latter quantity represents the water's colour as it might be perceived by the human eye (trichromatic colour vision); it is easily calculated from the shape of the spectrum. These new formulas are based on a combined dataset. Most of the data were obtained in the specific, optically complex environment of the Baltic Sea. Additional data, taken from the NASA bio-Optical Marine Algorithm Dataset (NOMAD) and representing various regions of the global oceans, were used to widen the potential applicability of the new formulas. We indicate the reasons why these simple empirical relationships can be derived and compare them with the results of straightforward modelling; possible applications are also described. We present, among other things, an example of a simple semi-analytical algorithm using both new empirical formulas. This algorithm is a modified version of the well-known quasi-analytical algorithm (QAA), and it can improve the results obtained in optically complex waters. This algorithm allows one to estimate the full spectra of the backscattering and absorption coefficients, without the need for any additional a priori assumptions regarding the spectral shape of absorption by dissolved and suspended seawater constituents.