Linux From Scratch is a "distribution" I've always wanted to try but never had time to build a system of my own. A couple of years ago, I used Gentoo for a few months as my main desktop. At that time it was a bit too much for my skills and I had difficulties in keeping a usable system together.
Linux From Scratch would be even more hard core solution. But the documentation is excellent and I think I might have enough time some weekend to build my own minimal system from the sources. But it is another thing to have a minimal system and a usable system installed in an old computer I would have for this experiment. A usable desktop would take some more evenings and a couple of weeks reading Beyond Linux from Scratch.
You can read the documentation for building your own system online. There is also a LiveCD available to be used as the host system when building LFS.