Generally you can compress data that has some sort of predictability or redundancy. Dictionary based compression (e.g. ZIP style algorithms) traditionally don't work well on small chunks of data because of the need to share the selected dictionary.
In the past, when I have compressed very small chunks of data with somewhat predictable patterns, I have used SharpZipLib with a custom dictionary. Rather than embed the dictionary in the actual data, I hard-coded the dictionary in every program that needs to (de)compress the data. SharpZipLib gives you both options: custom dictionary, and keep dictionary separate from the data.
Again this will only work well if you can predict some patterns to your data ahead of time so that you can create an appropriate compression dictionary, and it's feasible for the dictionary itself to be separate from the compressed data.