This study examined variations of a nonequivalent groups equating design used with constructed-response (CR) tests to determine which design was most effective in producing equivalent scores across the two tests to be equated. Using data from a large-scale exam, the study investigated the use of anchor CR item rescoring in the context of classical equating methods. Four linking designs were examined: (a) an anchor set containing common CR items, (b) an anchor set incorporating common CR items rescored, (c) an external multiple-choice (MC) anchor test, and (d) an equivalent groups design incorporating CR items rescored (no anchor test). The use of CR items without rescoring or the use of an external MC anchor resulted in much larger bias than the other two designs. The use of a rescored CR anchor and the equivalent groups design led to similar levels of equating error.