tree down in my yard

[dahdahdahdancer.livejournal.com]

In last night's storm a tree came down in my yard (it's my tree, not my neighbor's, not the city's), and it did a slight bit of damage to a raised garden bed but no big deal. Since this is my first tree-downing, I'm looking for advice on the best and least expensive way to get rid of it. I talked to the city's tree guys, who say that because it's on private property, they can't help. I fear if I get the company that insures my property involved, they'll raise my rates.