We describe a novel Lempel-Ziv approach suitable for compressing structured documents, called LZCS, which takes advantage of redundant information that can appear in the structure. The main idea is that frequently repeated subtrees may exist and these can be replaced by a backward reference to their first occurence. The main advantage is that compressed documents generated by LZCS are easy to display, access at random, and navigate. In a second stage, processed documents can be further compressed using some semiadaptive technique, so that random access and navigability remain possible. LZCS is especially efficient to compress collections of highly structured data, such as XML forms, invoices, e-commerce and web-service exchange documents. The comparison against structure-based and standard compressors shows that LZCS is a competitive choice for this type of documents, while the others are not well-suited to support navigation or random access.