Handy link/tip Raphaelle.
I was having the reverse of your problem with fading text. Apparently from 0.99 to 1 opacity, anti-aliasing is handed over from the browser to the OS. You end up with a visible popping effect.
To avoid that I'm just fading up to 0.99, there's no popping but the text looks naff.
Using this instead has helped a lot.
Sorry I couldn't help, but thanks for the link.
text-shadow: 0 0 0 #aaa; /* instead of the #000 for thinner trick */
-webkit-text-shadow: 0 0 0 #aaa;
-moz-text-shadow: 0 0 0 #aaa;