Web archives, query and proxy logs, and so on, can all be very large and highly repetitive; and are accessed only sporadically and partially, rather than continually and holistically. This type of data is ideal for compression-based archiving, provided that random-access to small fragments of the original data can be achieved without needing to decompress everything. The recent RLZ (relative Lempel Ziv) compression approach uses a semi-static model extracted from the text to be compressed, together with a greedy factorization of the whole text encoded using static integer codes. Here we demonstrate more precisely than before the scenarios in which RLZ excels. We contrast RLZ with alternatives based on block-based adaptive methods, including approaches that "prime" the encoding for each block, and measure a range of implementation options using both hard-disk (HDD) and solid-state disk (SSD) drives. For HDD, the dominant factor affecting access speed is the compression rate achieved, even when this involves larger dictionaries and larger blocks. When the data is on SSD the same effects are present, but not as markedly, and more complex trade-offs apply.