New absorption, linear dichroism (LD) and circular dichroism (CD) measurements at low temperatures on the Fenna-Matthews-Olson complex from Prosthecochloris aestuarii are presented. Furthermore, the anisotropy of fluorescence excitation spectra is measured and used to determine absolute LD spectra, i.e. corrected for the degree of orientation of the sample. In contrast to previous studies, this allows comparison of not only the shape but also the amplitude of the measured spectra with that calculated by means of an exciton model. In the exciton model, the point-dipole approximation is used and the calculations are based on the trimeric structure of the complex. An improved description of the absorption and LD spectra by means of the exciton model is obtained by simply using the same site energies and coupling strengths that were given by Louwe et al. (1997, J Phys Chem B 101: 1128011287) and including three broadening mechanisms, which proved to be essential: Inhomogeneous broadening in a Monte Carlo approach, homogeneous broadening by using the homogeneous line shape determined by fluorescence line-narrowing measurements [Wendling et al. (2000) J Phys Chem B 104: 5825-5831] and lifetime broadening An even better description is obtained when the parameters are optimized by a global fit of the absorption, LD and CD spectra. New site energies and coupling, strengths are estimated. The amplitude of the LD spectrum is described quite well. The shape of the CD spectrum is modelled in a satisfactory way but its size can only be simulated by using a rather large value for the index of refraction of the medium surrounding the chromophores. It is shown that the estimated coupling strengths are compatible with the value of the dipole strength of bacteriochlorophyll a, when using the empty-cavity model for the local-field correction factor.