As an attempt to combine extractive and abstractive summarization, Sentence Rewriting models adopt the strategy of extracting salient sentences from a document first and then paraphrasing the selected ones to generate a summary. However, the existing models in this framework mostly rely on sentence-level rewards or suboptimal labels, causing a mismatch between a training objective and evaluation metric. In this paper, we present a novel training signal that directly maximizes summary-level ROUGE scores through reinforcement learning. In addition, we incorporate BERT into our model, making good use of its ability on natural language understanding. In extensive experiments, we show that a combination of our proposed model and training procedure obtains new state-of-the-art performance on both CNN/Daily Mail and New York Times datasets. We also demonstrate that it generalizes better on DUC-2002 test set.