This report examines how selection fairness is influenced by the characteristics of a selection instrument in terms of its distribution of item difficulties, level of item discrimination, degree of item bias, and testing strategy. Computer simulation was used in the administration of either a conventional or Bayesian adaptive ability test to a hypothetical target population consisting of a minority and majority subgroup. Fairness was evaluated by three indices which reflect the degree of differential validity, errors in prediction (Cleary's model), and proportion of applicants exceeding a selection cutoff (Thorndike's model). Major findings are: (1) when used in conjunction with either the Bayesian or conventional test, differential prediction increased fairness and facilitated the interpretation of the fairness indices; (2) the Bayesian adaptive tests were consistently fairer than the conventional tests for all item pools above the alpha=.7 discrimination level for tests of more than 30 items; (3) the differential prediction version of the Bayesian adaptive test produced almost perfectly fair performance on all fairness indices at high discrimination levels; and (4) the placement of subgroup prior distribution in the Bayesian adaptive testing procedure can affect test fairness. (Author/CTM)