We had tons of PI on our property and last spring I used extra strength Round up (I believe it was for more "woody" plants. In essence I did what Dave is recommending above, applying it when it was just beginning to leaf and spread. It worked pretty well, getting rid of about 75% of the large patches that we had. It worked very well on large vines that had grown high into some trees. I cut the vine low and sprayed the stump with Roundup. It killed it completely.
