Entropy minimization has been widely used in unsupervised domain adaptation (UDA). However, existing works reveal that the use of entropy-minimization-only may lead to collapsed trivial solutions for UDA. In this article, we try to seek possible close-to-ideal UDA solutions by focusing on some intuitive properties of the ideal domain adaptation solution. In particular, we propose to introduce diversity maximization for further regulating entropy minimization. In order to achieve the possible minimum target risk for UDA, we show that diversity maximization should be elaborately balanced with entropy minimization, the degree of which can be finely controlled with the use of deep embedded validation in an unsupervised manner. The proposed minimal-entropy diversity maximization (MEDM) can be directly implemented by stochastic gradient descent without the use of adversarial learning. Empirical evidence demonstrates that MEDM outperforms the state-of-the-art methods on four popular domain adaptation datasets.