Originally Posted by JesperP
By making a small starter every time and save slurry from that I suspect I could keep the yeast cleaner and fresher.
That is correct, however, keep in mind that some strains will start to mutate after 6 - 8 generations and will start to produce off flavors.
With your first fresh, unused starter, make it double the normal size, decant and pour into 1/2 pint jars (usually 4) leaving enough to make your beer for the day. With those 4, you can make 4 more from each then 4 more from those and so on... Until you get to the 6 - 8th generation.. I think it comes out to about 4096 uses on the 6th gen.
1st gen - 4 1/2 pint jars
2nd gen - 16
3rd gen - 64
4th gen - 256
5th gen - 1024
6th gen - 4096
I use Platinum strains from White Labs (limited releases) so I make them last at least a year by doing this..