In compressing large datasets it is often desirable to guarantee locality properties that allow the efficient decoding and efficient update of short fragments of data. This paper proposes a universal compression scheme for memoryless sources with the following features: 1. the rate can be made arbitrarily close to the entropy of the underlying source, 2. constant-sized (as a function of the blocklength) fragments of the source can be recovered by probing a constant number of codeword bits on average, 3. the update of constant-sized fragments of the source can be achieved by reading and modifying a constant number of codeword symbols on average, and 4. the overall encoding and decoding complexity is quasilinear in the blocklength of the source. © 2019 IEEE.