Corresponding to the Glimm-Effros dichotomy for Borel equivalence relations there is a version for coanalytic equivalence relations by Hjorth: either E_0 embeds into the equivalence relation, or there is a \Delta1_3 function which assigns countable subsets of \omega_1 as complete invariants, assuming x^# exists for every real x. Here equivalence in E_0 means that the reals are the same in all but finitely many digits. We sketch the proof and show that the conclusion holds for \Delta1_2 equivalence relations as well. We also discuss versions for more complicated sets.