If you lay the batts perpendicular to the rafters and over the old, you have created a nightmare if you ever want to get to an area in your attic unless you build a catwalk at this time. Going over the rafters , you will not know where to walk in case of an emergency.
I would do as one suggested, clean up the crap and lay them down in between the rafters. If you rafters are 24"oc, then get the 22 inch stuff, don't put 15 inch in 24 " spaces. Too much loose space.