Sure it's possible. For example, to use Zlib compression, specify the following in the output hints field (Format Hints section):
compression-codec zlib+sh
LZ4HC is an alternative compression algorithm, much faster than Zlib for decompression with slightly lower compression ratios:
compression-codec lz4hc+sh
You can do the same with all tools that provide an output hints parameter. For a list of all format hints available, open the Format Explorer window, select the desired format, and double click the implementation tree item.