Duplicate "randomness" in random-based FX

Randomly curves and distorts path segments inward and outward.

It looks as though random is different every time an instance of the Tweak effect is applied. So I can have a rectangle, apply Tweak, and have another identical rectangle and apply Tweak to it too, and they will look different!

I want to copy the "randomness" of Tweak from my rectangle to another identical rectangle so they will look exactly the same when Tweak is applied. The only way I have found is to duplicate the rectangle with Tweak already applied to it. Is there any other way that I could duplicate the Tweak effect (and its randomness) without duplicating the entire object it was applied to?

This is in CS4.

Thanks.