Most Twitter search systems generally treat a tweet as a plain text when modeling relevance. However, a series of conventions allows users to tweet in structural ways using combination of different blocks of texts. These blocks include plain texts, hashtags, links, mentions, etc. Each block encodes a variety of communicative intent and sequence of these blocks captures changing discourse. Previous work shows that exploiting the structural information can improve the structured document (e.g., web pages) retrieval. In this paper we utilize the structure of tweets, induced by these blocks, for Twitter retrieval. A set of features, derived from the blocks of text and their combinations, is used into a learning-to-rank scenario. We show that structuring tweets can achieve state-of-the-art performance. Our approach does not rely upon social media features, but when we do add this additional information, performance improves significantly.