In this paper, we introduce a syntax-based sentence simplifier that models simplification using a probabilistic synchronous tree substitution grammar (STSG). To improve the STSG model specificity we utilize a multi-level backoff model with additional syntactic annotations that allow for better discrimination over previous STSG formulations. We compare our approach to T3 (Cohn and Lapata, 2009), a recent STSG implementation, as well as two state-of-the-art phrase-based sentence simplifiers on a corpus of aligned sentences from English and Simple English Wikipedia. Our new approach performs significantly better than T3, similarly to human simplifications for both simplicity and fluency, and better than the phrasebased simplifiers for most of the evaluation metrics.