Thanks guys.
Well, what I lack in patience - I make up for in foolishness.
I found the posts earlier in this thread about cleaning pennants and decided to give it a go because the Tigers pennant is fairly cheap and I wanted to practice. I'm pretty pleased with the result.
What may not have been obvious from the "before" photo was some pretty bad discoloration above the tiger and at the tip.
I covered the spine and laid the pennant flat in the bath and then sprayed the bleach. Then I ran it under the faucet to rinse it off. I think next time, I'll tape it on the shower wall like Rob suggests. The black ink ran a little bit, but as others mentioned I used copious amounts of water and that rinsed off with no problem.
I think I've now achieved blissful over-confidence so I'll probably gamble with the Yankees pennant. The photo on the pennant looks to be fastened with staples so I don't think it will be too tough to get if off for cleaning.