We consider the following full-text search autocompletion feature. Imagine a user of a search engine typing a query. Then with every letter being typed, we would like an instant display of completions of the last query word which would lead to good hits. At the same time, the best hits for any of these completions should be displayed. Known indexing data structures that apply to this problem either incur large processing times for a substantial class of queries, or they use a lot of space. We present a new indexing data structure that uses no more space than a state-of-the-art compressed inverted index, but with 10 times faster query processing times. Even on the large TREC Terabyte collection, which comprises over 25 million documents, we achieve, on a single machine and with the index on disk, average response times of one tenth of a second. We have built a full-fledged, interactive search engine that realizes the proposed autocompletion feature combined with support for proximity search, semi-structured (XML) text, subword and phrase completion, and semantic tags.