From calibrated, weakly scattering tissue phantoms (2-6 mm-1), we extract the attenuation coefficient with an accuracy of 0.8 mm-1 from OCT data in the clinically relevant 'fixed focus' geometry. The data are analyzed using a single scattering model and a recently developed description of the confocal point spread function (PSF). We verify the validity of the single scattering model by a quantitative comparison with a multiple scattering model, and validate the use of the PSF on the calibrated samples. Implementation of this model for existing OCT systems will be straightforward. Localized quantitative measurement of the attenuation coefficient of different tissues can significantly improve the clinical value of OCT.