Document retrieval structures index a collection of string documents, to retrieve those that are relevant to query strings p: document listing retrieves all documents where p appears; top k retrieval retrieves the k most relevant of those. Classical structures use too much space in practice. Most current research uses compressed suffix arrays, but fast indices still use 17-21 bpc (bits per character), whereas small ones take milliseconds per returned answer. We present the first document retrieval structures based on Lempel-Ziv compression, precisely LZ78. Our structures use 7-10 bpc and dominate a large part of the space/time tradeoffs. They also enable more efficient partial or approximate answers: our document listing outputs the first 75%-80% of the answers at a rate of one per microsecond; for top-k retrieval we return a result of 90% quality at the same rate and using just 4-6 bpc. This outperforms current indices by a wide margin. (C) 2019 Elsevier Inc. All rights reserved.