A computer is programmed to compress data of a database in response to database modification language (DML) statements generated by on-line transaction processing (OLTP) systems. In several embodiments, data that is initially added to a database block is left uncompressed until a predetermined condition is satisfied, which happens infrequently (relative to OLTP transactions on the block). When satisfied, the computer automatically compresses all uncompressed data in the block, which increases the amount of unused space in the block. New data is thereafter added uncompressed to the partially compressed block, until satisfaction of a predetermined condition whereby the partially compressed block is again compressed, i.e. re-compressed. Adding of new data to a partially compressed block and its compression are repeated unless another predetermined condition is met, in response to which the block is not further re-compressed, thereby to recognize a limit on the benefit from compression.