Good news...so should I negotiate?

[Ludwig von Dracula]

I had pretty much decided on one program that was offering an OK-ish funding package--all but $1000 of tuition covered (something about me being an international student), along with most fees, and a stipend that would leave me with about $8000 left for living expenses after taking care of the other academic costs. Then yesterday, I hear back from two other schools with funding packages. One is also in the States, and is offering slightly more than the one I'd almost decided to attend. The other is my current institution, which has offered four years at their highest level of funding.

I'm definitely not bemoaning my good fortune! Luckily, I still have about a week to decide. I still favour the first school--I like their faculty and I already feel emotionally invested in the program (risky, of course). I've emailed most of the faculty and some students already. I'm trying to figure out if I should try to negotiate with them based on my better offers. Or will this only hurt my case? What have you done in such situations?