In this study we examined variations of the nonequivalent groups equating design for 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. Using data from a large-scale exam, this study investigated the use of anchor CR item rescoring (known as trend scoring) in the context of classical equating methods. Four linking designs were examined: an anchor with only MC items, a mixed-format anchor test containing both MC and CR items; a mixed-format anchor test incorporating common CR item rescoring; and an equivalent groups (EG) design with CR item rescoring, thereby avoiding the need for an anchor test. Designs using either MC items alone or a mixed anchor without CR item rescoring resulted in much larger bias than the other two designs. The EG design with trend scoring resulted in the smallest bias, leading to the smallest root mean squared error value.