There are many HTML compression extensions for TYPO3 in the TER. Many of them aren't maintained anymore or just have a huge overhead, you will mostly not need for anything. So why not build a content compression by your own?
It's pretty easy to implement. Basically it just require the use of two Hooks from
tslib/class.tslib_fe.php. The Hooks are called
contentPostProc-output. The first one handles normal pages with cached output, the second one does the same, just for uncached pages with
USER_INT objects. This Hooks will be bind to a
function of your choice in
ext_localconf.php of your extension.