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This work addresses the unsupervised domain adaptation problem, especially in the case of class labels in the target domain being only a subset of those in the source domain. Such a partial transfer setting is realistic but challenging and existing methods always suffer from two key problems, negative transfer and uncertainty propagation. In this paper, we build on domain adversarial learning and propose a novel domain adaptation method BA$^3$US with two new techniques termed Balanced Adversarial Alignment (BAA) and Adaptive Uncertainty Suppression (AUS), respectively. On one hand, negative transfer results in misclassification of target samples to the classes only present in the source domain. To address this issue, BAA pursues the balance between label distributions across domains in a fairly simple manner. Specifically, it randomly leverages a few source samples to augment the smaller target domain during domain alignment so that classes in different domains are symmetric. On the other hand, a source sample would be denoted as uncertain if there is an incorrect class that has a relatively high prediction score, and such uncertainty easily propagates to unlabeled target data around it during alignment, which severely deteriorates adaptation performance. Thus we present AUS that emphasizes uncertain samples and exploits an adaptive weighted complement entropy objective to encourage incorrect classes to have uniform and low prediction scores. Experimental results on multiple benchmarks demonstrate our BA$^3$US surpasses state-of-the-arts for partial domain adaptation tasks. Code is available at \url{https://github.com/tim-learn/BA3US}.