Negotiating mathematics postdoc salary when having an offer with higher salary I recently won an NSF mathematical Science Postdoctoral Research Fellowship at University 1. At this University, the math NSF postdocs have a have a much lower salary and benefits than regular "named postdocs" (XYZ Assistant Professor)and during their 2 years of half-time NSF support teach two thirds the amount (despite only half the salary coming from the university). I did not get a regular postdoc offer from Uni 1.

At the same time, I have a 3 year postdoc offer from a fancy institute at US University 2, with significantly higher salary than regular postdocs at Uni 1 (which is already much higher than NSF postdocs at Uni 1), more travel funding than the NSF MSPRF, and NO teaching unless I want to.

Research wise, Uni 1 is a better fit.
Would it be reasonable for me to leverage the Uni 2 offer to perhaps convince Uni 1 to raise my salary during my NSF postdoc there to the level of their regular postdocs and maybe give me the title of a regular postdoc at Uni 1 for one or two years when I am there?
Or perhaps reduction in the number of courses I have to teach?
If so, does one go about it?
I think that there is a difference between University 1 wanting you, and having you because you come with an NSF. That makes a huge difference in whether you can leverage for a higher salary or not.

The fact that University 1 did not offer you their regular postdoc title sounds like a hint to me that they will probably not be up for negotiation. Though, it doesn't hurt to try.