Log data records important runtime information about the running of a software system for different purposes including performance assurance, capacity planning, and anomaly detection. Log management tools such as ELK Stack and Splunk are widely adopted to manage and leverage log data in order to assist DevOps in real-time log analytics and decision making. To enable fast queries and to save storage space, such tools split log data into small blocks (e.g., 16KB), then index and compress each block separately. Previous log compression studies focus on improving the compression of either large-sized log files or log streams, without considering improving the compression of small log blocks (the actual compression need by modern log management tools). The evaluation of four state-of-the-art compression approaches (e.g., Logzip, a variation of Logzip by pre-extracting log templates named Logzip-E, LogArchive and Cowic) indicates that these approaches do not perform well on small log blocks. In fact, the compressed blocks that are preprocessed using Logzip, Logzip-E, LogArchive or Cowic are even larger (on median 1.3 times, 1.5 times, 0.2 times or 6.6 times) than the compressed blocks without any preprocessing. Hence, we propose an approach named LogBlock to preprocess small log blocks before compressing them with a general compressor such as gzip, deflate and lz4, which are widely adopted by log management tools. LogBlock reduces the repetitiveness of logs by preprocessing the log headers and rearranging the log content leading to an improved compression ratio for a log file. Our evaluation on 16 log files shows that, for 16KB to 128KB block sizes, the compressed blocks by LogBlock are on median 5 to 21 percent smaller than the same compressed blocks without preprocessing (outperforming the state-of-the-art compression approaches). LogBlock achieves both a higher compression ratio (a median of 1.7 to 8.4 times, 1.9 to 10.0 times, 1.3 to 1.9 times and 6.2 to 11.4 times) and a faster compression speed (a median of 30.8 to 49.7 times, 42.6 to 53.8 times, 4.5 to 6.0 times and 2.5 to 4.0 times) than Logzip, Logzip-E, LogArchive and Cowic. LogBlock can help improve the storage efficiency of log management tools.