(I keep the tea in, too, unless it's a green or herbal tea -- tea travesty unite!!)
That's interesting, then. I have found that some teas (rooibos in general for some reason) just come through the ball. It doesn't really bother me, though, I'm okay drinking a few stems.
I use a one cup French Press coffee maker when I only want one cup of tea. Something like this but this isn't the one I have. I got mine from Target. I hate tea balls. They never do a good job, and I usually make my tea with more than the "recommended" amount of loose tea. Also, it's better for the tea if it has room to expand, and most tea balls don't give enough space for the tea to do that.
ETA: Teavana has some cool looking products these days! I haven't been to their site in ages but some of their stuff looks like it would better suit your needs than that tea ball.