I 2nd the "bigger bag target" idea by Greg... inside of 15 yards there would have to be major malfunction to miss the whole bag, especially the big Morrell bag.
When I got my new bow in '05, I had a medium sized bag target. I put a paper plate on the target with a circle about 6 inches in diameter. I started at 10 yards and I would not let my self move back until I had 6 arrows in a row in that circle. Then I would move back 5 yards and go again.
I always used straw as a back drop in my younger years... but couldn't stand the mess in the yard and the pain in the ass it was to haul them away when they are water logged all to hell and come a part.
My cousin on the other hand has enough back yard to where if you miss high/left/right you are still going to have the arrow in the yard. Top that with a chocolate lab that when you tell her to "fetch it up" will go find the arrow that is buried in the ground for you.