Dodeen (2004) studied the correlation between the item parameters of the three-parameter logistic model and two item fit statistics, and found some linear relationships (e.g., a positive correlation between item discrimination parameters and item fit statistics) that have the potential for influencing the work of practitioners who employ item response theory. This paper examines the same type of linear relationships as studied in Dodeen. However, this paper adds to the literature by employing item fit statistics not considered in Dodeen, which have been recently suggested and whose Type I error rates have been demonstrated to be generally close to the nominal level. Detailed simulations show that if one uses certain of the recently suggested item fit statistics, there is no need to worry about any linear relationships between the item parameters and item fit statistics.