over the last 7 yrs. I have slowly been reclaiming old farmland and killing off poison ivy/oak, prickers, and bittersweet! The best method that is pretty natural so far is this way (as I've been testing for several yrs now anyway):

I cut down the weeded area and lay the clippings/cuttings down and any other raked up debris like old leaves and branches where I want my newest bed to be (over ivy site). Next I place freshly cleaned out chicken coop and duck coop bed onto pile. Then I put heavy cardboard feedbags or really thick layer of newspapers on top. Next I put my old composted material on top and cover all with a sawdust mulch (from my DH's sawmill). Then I wait only about a month and plant on top of it. The next year my plants are always thriving on the site without signs of bad things growing....so far so good!!!!!!

hope this helps you. I have always layered...its nothing new and has been around many years before the writing of the lasagna book! thank goodness for neighbors and back copies of mother earth/organic gardening/etc....