Computerized adaptive testing tends to select and present items frequently with high discrimination parameters. This tendency leads to bias of item exposure. To address this shortcoming, we propose difficulty constrained uniform adaptive testing. During the first stage, the method selects and presents the optimal item from a uniform item group generated by a state-of-the-art uniform test assembly technique. In the second stage, the method selects and presents the optimal item with a difficulty parameter value within the neighborhood of the examinee's ability estimate from the whole item pool. Numerical experiments results underscore the effectiveness of the proposed method.