When test-takers are offered a choice of essay questions, some questions may be harder than others. If the test includes a common portion taken by all test-takers, an adjustment to the scores is possible. Previously proposed adjustment procedures disregard the test-makers' efforts to create questions of equal difficulty; these procedures tend to make larger adjustments when the scores to be adjusted are less correlated with scores on the common portion. This paper suggests an adjustment procedure that makes smaller adjustments when the correlation between the scores to be adjusted and the scores on the common portion is weak. The paper includes a derivation of the adjustment formula and a numerical example of the resulting adjustment. The numerical example uses groups taking an Advanced Placement history test, with group sizes of 3,411; 38,445; 1,390; 10,382; and 5,180. The basis for the solution is to impute a score for the test-taker on each alternate question the test-taker did not answer, and then average the scores, observed and imputed, over all the alternative questions. (Contains two tables and four references.) (Author/SLD)