This paper presents a new heuristic approach to interactive test assembly that is called the successive item replacement algorithm. This approach builds on the work of W. J. van der Linden (1987) and W. J. van der Linden and E. Boekkooi-Timminga (1989) in which methods of mathematical optimization are combined with item response theory to construct tests from larger collections or pools of items. This new approach is contrasted with two more formal models and other heuristic approaches that appear in the literature. An experiment using quasi-realistic data is performed that serves to illustrate the difference in approaches for typical practical test construction applications. Three tables and three figures illustrate the discussion. (Contains 14 references.) (Author/SLD)