What would you say for some even lower compression ratios?
What about a way to estimate the Shannon entropy of your data??
Why not give PAQ8PX a try then???
Yeah of course I am exaggerating a bit but the PAQ8 compressor series will definitely give you the best lossless compression ratios you can currently get on Earth. Actually PAQ8PH series have won the Hutter prize twice!
PAQ8PH contain dictionaries in them and aim at compressing text. For "everyday" usage the PAQ8PX is likely the best you can find out there. The only tiny winy drawback is that it is awfully slow: just a bit faster than a PSTN line on my CPU.
In any case, be it practical or not, you should give PAQ8PX a try and I just made your life a bit easier by making a simple frontend called FrontPAQ that simplifies the compression level selection and also calculates the ETA, the compression speed and some more things. FrontPAQ includes the latest version of PAQ8PX I could find (I found it in this post), is written in AutoIt \m/ so it is a standalone executable and is realeased under the GNU GPL v3.
Here are some screenshots showing the whole process you have to follow in order to compress a directory:
(Don't worry, normally you will get more than 3.8KB/s)
So, go on and download FrontPAQ from here.