We report on a new and improved version of high-order entropy-compressed suffix arrays, which has theoretical performance guarantees comparable to previous work, yet represents an improvement in practice. Our experiments indicate that the resulting text index offers state-of-the-art compression. In particular, we require roughly 20% of the original text size--without requiring a separate instance of the text--and support fast and powerful searches. To our knowledge, this is the best known method in terms of space for fast searching. We can additionally use a simple notion to encode and decode block-sorting transforms (such as the Burrows-Wheeler transform), achieving a slightly better compression ratio than bzip2. We also provide a compressed representation of suffix trees (and their associated text) in a total space that is comparable to that of the text alone compressed with gzip.