Jefro was on the right track.
Puppy, which is what I mainly use as my 'daily driver', is, AFAIK, the
only Linux distro in existence capable of saving back to the very same optical disc that its 'Live' install runs from.....
so long as you do not 'close' (or 'finalize') the disc when creating it.
This being the case, obviously a DVD will be preferable to a CD, due to it's much larger capacity.
The Puppy Forums @ murga-linux.com run a special sub-forum dedicated solely to those users that prefer to run Puppy in this manner....a surprising number, in fact.
http://www.murga-linux.com/puppy/index.php?f=6
Even Knoppix can't do this.
Most of the 'buntu flavours will create persistence for you,
if you run them from a 'LiveUSB'.....especially if you use
UNetBootin to create the USB 'key'.
Mike.