This study examined variations of the nonequivalent-groups equating design for mixed-format tests--tests containing both multiple-choice (MC) and constructed-response (CR) items--to determine which design was most effective in producing equivalent scores across the two tests to be equated. Four linking designs were examined: (a) an anchor with only MC items; (b) a mixed-format anchor containing both MC and CR items; (c) a mixed-format anchor incorporating CR item rescoring; and (d) a hybrid combining single-group and equivalent-groups designs, thereby avoiding the need for an anchor test. Designs using MC items alone or those using a mixed anchor without CR item rescoring resulted in much larger bias than the other two design approaches. The hybrid design yielded the smallest root mean squared error value.