Severance offer, what should I ask for?

The company sent a severance agreement with a release of claims, and I am unsure what to do. It includes health coverage for a couple of months. Did anyone negotiate and succeed?

Thanks for writing this out. I went through something close to it 14 months ago, and it settled down once I kept a simple log of every call and form.

Ask for the offer in writing and do not sign on the spot. A day or two to think is normal.