The ability to read a document depends on the reader’s skills and the text’s readability level. In this paper, we propose a system that uses deep learning techniques to simplify texts in order to match a reader’s level. We use a novel approach with a reinforcement learning loop that contains a readability classifier. The classifier’s output is used to decide if more simplification is needed, until the desired readability level is reached. The simplification models are trained on data annotated with readability levels from the Newsela corpus. Our simplification models perform at sentence level, to simplify each sentence to meet the specified readability level. We use a version of the Newsela corpus aligned at the sentence level. We also produce an augmented dataset by automatically annotating more pairs of sentences using a readability-level classifier. Our text simplification models achieve better performance than state-of-the-art techniques for this task.