Phrase queries play an important role in web search and other applications. Traditionally, phrase queries have been processed using a positional inverted index, potentially augmented by selected multi-word sequences (e.g., n-grams or frequent noun phrases). In this work, instead of augmenting the inverted index, we take a radically different approach and leverage the forward index, which provides efficient access to compact representations of documents. Modern retrieval systems maintain such a forward index, for instance, to generate snippets or compute proximity features. We present extensions of the established term-at-a time and document-at-a-time query-processing methods that make effective combined use of the inverted index and the forward index. Our experiments on two real-world document collections using diverse query workloads demonstrate that our methods improve response time both on main-memory and disk-based search engines with no additional index space.