Single-molecule FRET experiments on freely diffusing rigid molecules frequently show FRET efficiency (E) distributions broader than those defined by photon statistics. It is often unclear whether the observed extra broadening can be attributed to a physical donor-acceptor distance (R-DA) distribution. Using double-stranded DNA (dsDNA) labeled with Alexa488 and Cy5 (or Alexa647) as a test system, we investigate various possible contributions to the E distribution width. On the basis of simultaneous analysis of donor and acceptor intensities and donor lifetimes, we conclude that dsDNA chain dynamics can be ruled out as a possible reason for the observed E distribution broadening. We applied a set of tools to demonstrate that complex acceptor dye photophysics can represent a major contribution to the E distribution width. Quantitative analysis of the correlation between FRET efficiency and donor fluorescence lifetime in 2D multiparameter histograms allows one to distinguish between broadening due to distinct FRET or dye species. Moreover, we derived a simple theory, which predicts that the apparent distance width due to acceptor fluorescence quantum yield variations increases linearly with physical donor-acceptor distance. This theory nicely explains the experimentally observed FRET broadening of a series of freely diffusing labeled dsDNA and dsRNA molecules. Accounting for multiple acceptor states allowed the fitting of experimental E distributions, assuming a single fixed donor-acceptor distance.