Search engines are an essential tool for modern life. We use them to discover new information on diverse topics and to locate a wide range of resources. The search process in all practical search engines is supported by an inverted index structure that stores all search terms and their locations within the searchable document collection. Inverted indexes are highly optimised, and significant work has been undertaken over the past fifteen years to store, retrieve, compress, and understand heuristics for these structures. In this paper, we propose a new self-organising inverted index based on past queries. We show that this access-ordered index improves query evaluation speed by 25%--40% over a conventional, optimised approach with almost indistinguishable accuracy. We conclude that access-ordered indexes are a valuable new tool to support fast and accurate web search.