I have a collection of good brushes (natural bristle) that I keep for
fine painting, such as varnishing. I just finished varnishing the new
woodwork in a room we remodeled, and spent a lot of time picking loose
hairs out of the varnish. I had the problem with both older and new
brushes, so I'm thinking there must be a problem with the way I clean or
store them, that makes the bristles brittle.

I clean them using thinner, then detergent, and finally fells naptha
soap. Then I let them dry and keep them on a shelf. I recall seeing a
device that suspended your brushes in, as I recall, kerosene, to
preserve them, but it never explained what to do when you want to use
one of these kerosene impregnated brushes; I didn't think wiping them
and then using them was a good idea as I didn't want to get kerosene on
my work, which left the option of cleaning them, then waiting for them
to dry before using them, which could take a lot of time.

So what is the best way to preserve a good brush so it doesn't leave
bristles in your work?