We show-through close-coupled quantum-scattering calculations that the cross section for fine-structure-changing collisions between excited P-2(3/2) and ground S-2(1/2) A atoms of the same species, where A = Rb or Cs, is very sensitive to the molecular potentials and spin-orbit matrix elements of the alkali-metal-dimer species. Spectroscopic studies of these species are needed to extract accurate parameters. New high-resolution photoassociation spectroscopy of trapped atoms could be used for this purpose.