When an examination consists in whole or part of constructed response test items, it is common practice to allow the examinee to choose a subset of the constructed response questions from a larger pool. It is sometimes argued that, if choice were not allowed, the limitations on domain coverage forced by the small number of items might unfairly affect some examinees. Alternatives, such as increasing test length or confining questions to a core curriculum, might discourage teachers because of practical considerations. In this consideration of whether allowing examinee choice is a sensible strategy, some of the pitfalls of allowing choice are described. Some experimental steps that can tell whether choice can be implemented fairly are discussed. A bleak picture of the use of examinee choice emerges. To make tests with choice fair requires equating the test forms generated by the tests for their differential difficulty. Accomplishing this requires some special data gathering effort or trust in assumptions about unobserved responses that, if true, obviate the need for choice. If test items can be equated successfully, the value of choice is removed for any but the most superficial sense. Eight tables and seven figures illustrate the discussion. (Contains 40 references.) (SLD)