Probability distribution analysis (PDA) [M. Antonik et al., J. Phys. Chem. B 2006, 110, 6970] allows one to quantitatively analyze single-molecule (SM) data obtained in Forster resonance energy transfer (FRET) or fluorescence polarization experiments. By taking explicitly background and shot noise contributions into account, PDA accurately predicts the shape of one-dimensional histograms of various parameters, such as FRET efficiency or fluorescence anisotropy. In order to describe complex experimental SM-FRET or polarization data obtained for systems consisting of multiple non-interconverting fluorescent states, several extensions to the PDA theory are presented. Effects of brightness variations and multiple-molecule events are considered independently of the detection volume parameters by using only the overall experimental signal intensity distribution. The extended PDA theory can now be applied to analyze any mixture, by using any a priori model or a model-free deconvolution approach based on the maximum entropy method (MEM). The accuracy of the analysis and the number of free parameters are limited only by data quality. Correction of the PDA model function for the presence of multiple-molecule events allows one to measure at high SM concentrations to avoid artifacts due to a very long measurement time. Tools such as MEM and combined mean donor fluorescence lifetime analysis have been developed to distinguish whether extra broadening of PDA histograms could be attributed to structural heterogeneities or dye artifacts. In this way, an ultimate resolution in FRET experiments in the range of a few Angstrom is achieved which allows for molecular Angstrom optics distinguishing between a set of fixed distances and a distribution of distances. The extended theory is verified by analyzing simulations and experimental data.