The case of adaptive testing under a multidimensional logistic response model is addressed. An adaptive algorithm is proposed that minimizes the (asymptotic) variance of the maximum-likelihood (ML) estimator of a linear combination of abilities of interest. The item selection criterion is a simple expression in closed form. In addition, it is shown how the algorithm can be adapted if the interest is in a test with a "simple information structure." The statistical properties of the adaptive ML estimator are demonstrated for a two-dimensional item pool with several linear combinations of the two abilities. (Contains 1 figure and 15 references.) (Author/SLD)