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There is a family of label modification approaches including self and non-self label correction (LC), and output regularisation. They are widely used for training robust deep neural networks (DNNs), but have not been mathematically and thoroughly analysed together. We study them and discover three key issues: (1) We are more interested in adopting Self LC as it leverages its own knowledge and requires no auxiliary models. However, it is unclear how to adaptively trust a learner as the training proceeds. (2) Some methods penalise while the others reward low-entropy (i.e., high-confidence) predictions, prompting us to ask which one is better. (3) Using the standard training setting, a learned model becomes less confident when severe noise exists. Self LC using high-entropy knowledge would generate high-entropy targets. To resolve the issue (1), inspired by a well-accepted finding, i.e., deep neural networks learn meaningful patterns before fitting noise, we propose a novel end-to-end method named ProSelfLC, which is designed according to the learning time and prediction entropy. Concretely, for any data point, we progressively and adaptively trust its predicted probability distribution versus its annotated one if a network has been trained for a relatively long time and the prediction is of low entropy. For the issue (2), the effectiveness of ProSelfLC defends entropy minimisation. By ProSelfLC, we empirically prove that it is more effective to redefine a semantic low-entropy state and optimise the learner toward it. To address the issue (3), we decrease the entropy of self knowledge using a low temperature before exploiting it to correct labels, so that the revised labels redefine low-entropy target probability distributions. We demonstrate the effectiveness of ProSelfLC through extensive experiments in both clean and noisy settings, and on both image and protein datasets.