Fluorescence resonance energy transfer (FRET) between a donor (D) and an acceptor (A) at the single-molecule level currently provides qualitative information about distance, and quantitative information about kinetics of distance changes. Here, we used the sorting ability of confocal microscopy equipped with alternating-laser excitation (ALEX) to measure accurate FRET efficiencies and distances from single molecules, using corrections that account for cross-talk terms that contaminate the FRET-induced signal, and for differences in the detection efficiency and quantum yield of the probes. ALEX yields accurate FRET independent of instrumental factors, such as excitation intensity or detector alignment. Using DNA fragments, we showed that ALEX-based distances agree well with predictions from a cylindrical model of DNA; ALEX-based distances fit better to theory than distances obtained at the ensemble level. Distance measurements within transcription complexes agreed well with ensemble-FRET measurements, and with structural models based on ensemble-FRET and x-ray crystallography. ALEX can benefit structural analysis of biomolecules, especially when such molecules are inaccessible to conventional structural methods due to heterogeneity or transient nature.