Why don't you rent a chipper for a day and turn it all into mulch. Free mulch and it keeps it out of the trash stream.
We thought about that, but it'd cost around $200 to get a wood chipper out to our house, and we can't really afford it right now. Lawn refuse bags are a mere $0.50 each.
The good news is, it's not going into the landfills--the special paper bags are separate, and get mulched by the city. They then sell this "Dillo Dirt" back to people for their gardens.