Several models for optimizing incomplete sample designs with respect to information on the item parameters are presented. The following cases are considered: (1) known ability parameters; (2) unknown ability parameters; (3) item sets with multiple ability scales; and (4) response models with multiple item parameters. The models are able to cope with hierarchical structures in the population of examinees as well as the domain of content, and allow for practical constraints with respect to such items as test content, curricular differences between groups, or time available for item administration. An example with test data from a national assessment study illustrates the use of the models. This methodology was applied to an imagined third study of the Dutch part of the Second Mathematics Study of the International Association for the Evaluation of Educational Achievement for the three subject areas of Geometry, Algebra, and Arithmetic for a sample of 400 seventh graders. The LANDO computer program was used to solve the models, illustrating their utility. (Author/SLD)