Shedding Madness

I have a recent addition to my home (4 year old girl that I got about
3 months ago), and she's shedding EVERYWHERE! It's not just because
it's Spring; she's been shedding tons since I got her (in the middle
of winter). She is an american shorthair, but seems to have a much
thicker coat than my "mutt" kitty. I no longer have bright clothing,
furniture, or carpet because the hair covers everything, and I've
noticed tumbleweed hairfluffs all over. I brush her almost daily, and
every time I get 3-4 large sized brushes FULL of hair (compressed so
much the prongs don't show through anymore), and I'm sure I could get
more but she gets tired of the brushing after that much. I try to
sweep/vacuum, but nothing can keep up with her shedding.

I changed her food to Eukanuba (better than what she was eating) when
I got her. Is 3 months enough to reduce shedding by getting her on a
better food? Does her thick hair mean she'll always shed this much?
Is there anything else I can do to reduce the shedding? I plan on
making SURE I brush her daily to help reduce it. I don't think there
is anything medically wrong, as she has been to the vet numerous times
(initial examination, another check-up, and then a spay). The vet
commented that she had a beautiful healthy coat and nothing seemed
wrong.

How, oh HOW, can I reduce this shedding?


Thanks in advance,
Ginni