Adaptive testing under a multidimensional logistic response model is addressed. An algorithm is proposed that minimizes the (asymptotic) variance of the maximum-likelihood estimator of a linear combination of abilities of interest. The criterion results in a closed-form expression that is easy to evaluate. In addition, it is shown how the algorithm can be modified if the interest is in a test with a "simple ability structure". The statistical properties of the adaptive ML estimator are demonstrated for a two-dimensional item pool with several linear combinations of the abilities.