We have fairly good soil. Down about 1 foot or so you hit the clay layer, then sand. I am worried about using the cardboard unless maybe I put it into my 33 gallon garbage can and soaked it well with water as Dave suggests. Stuff just doesn't rot all that fast here. It could take years to break down. Paper, scraps, small twigs might work but even the twigs would take a long time to break down unless it is half rotten to begin with. I have those two bags of last years stuff in black bags and am hoping it is really rotten in there. Going to leave it in the black bags until the yard is dug up and ready. Maybe rotten kitchen stuff on bottom, then really wet (as in soggy) cardboard, then detritus from last year, then leaves I packed my rhody's in over winter to prevent wind and sunburn, then compost, thennnnnn soil. Surely that will work. It will be the middle of June before I think we can do this. If you dig down a foot you hit ice even then. Course, that wouldn't prevent ripping up the sod.