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I'm using a number of jQueryUI accordions on a single page inside of AnythingSlider. It used to be that it was pretty smooth, but has gotten jerky.
Now, instead inserting a bunch of code, how about I just give the link and you can look. If it works fine for you, then, well, I just don't know. Of course, if there's more you'd like to have, let me know.
I've got an aged laptop that sometimes lags behind my year-old Android phone. Your accordions looked slick in Chrome, a little less so in FireFox, and the site was utterly trashed and unintelligible in IE7.
Seems to work fin, smooth and all.