It is unrealistic to suppose that standard item response theory (IRT) models will be appropriate for all of the new and currently considered computer-based tests. In addition to developing new models, we also need to give some attention to the possibility of constructing and analyzing new tests without the aid of strong models. Computerized adaptive testing currently relies heavily on IRT. Alternative, empirically based, nonparametric adaptive testing algorithms exist, but their properties are little known. This paper introduces a nonparametric, tree-based algorithm for adaptive testing and shows that it may be superior to conventional, IRT-based adaptive testing in cases where the IRT assumptions are not satisfied. In particular, it shows that the tree-based approach clearly outperformed (one-dimensional) IRT when the pool was strongly two-dimensional.