Dead standing tree. EEEK!

Theres an enormous old sweetgum in my back yard that has been dead for more than 5 years and looms over a large portion of the arable land back there. Its not in danger of hitting any structures when it falls, but Id like to get it on the ground so that I can start utilizing that part of the yard without constantly worrying about it. Its got some sprawling branches that I was very worried about falling during the felling process, but I just ran a cord up to one of them and shook the piss out of the tree (hoping to pull some branches down so I could more safely fell it) I got all the major branches shaking pretty good, but nothing fell. It makes me think that I could safely get it on the ground. Thoughts?