When tests contain few items, observed score may not be an accurate reflection of true score, and the Mantel Haenszel (MH) statistic may perform poorly in detecting differential item functioning. Applications of the MH procedure in such situations require an alternate strategy; one such strategy is to include background variables in the matching criterion. Techniques for incorporating external information are presented here that match on a weighted score that combines the observed score and background data, using either ordinary least squares regression or a multilevel model. The regression and multilevel models were constructed using data obtained with the Grade 3 North Carolina End of Grade Mathematics Test. A simulation study was performed in which the prediction models were used to generate data, and three MH statistics were computed matching on observed scores, regression weighted scores, and multilevel weighted scores. The results showed similar performance for the regression and multilevel weighted score methods. The observed score and weighted score methods demonstrated advantages over the observed score method for test lengths of 5 and 10 items, but the improvement was small and inconsistent. Techniques for improving the performance of the weighted score methods are discussed. (Contains 21 references and 12 tables.) (SLD)