In equating, when common items are internal and scoring is conducted in terms of the number of correct items, some pairs of total scores ("X") and common-item scores ("V") can never be observed in a bivariate distribution of "X" and "V"; these pairs are called "structural zeros." This simulation study examines how equating results compare for different approaches to handling structural zeros. The study considers four approaches: the no-smoothing, unique-common, total-common, and adjusted total-common approaches. This study led to four main findings: (1) the total-common approach generally had the worst results; (2) for relatively small effect sizes, the unique-common approach generally had the smallest overall error; (3) for relatively large effect sizes, the adjusted total-common approach generally had the smallest overall error; and, (4) if sole interest focuses on reducing bias only, the adjusted total-common approach was generally preferable. These results suggest that, when common items are internal and log-linear bivariate presmoothing is performed, structural zeros should be maintained, even if there is some loss in the moment preservation property.