Items with the highest discrimination parameter values in a logistic item response theory (IRT) model do not necessarily give maximum information. This paper shows which discrimination parameter values (as a function of the guessing parameter and the distance between person ability and item difficulty) give maximum information for the three-parameter logistic IRT model. The optimal discrimination parameter value is shown to be inversely related to the distance between item difficulty and person ability. An upper bound for the information as a function of these parameters is derived; and this upper bound is used to formulate a fast item selection algorithm for adaptive testing. In a small simulation study this algorithm was one and one half to six times as fast as an algorithm in which the information of all items in an item bank is calculated. (Contains 1 table, 6 figures, and 9 references.) (Author/SLD)