Admit to additional crimes in exchange for a lighter sentence? How does that work?

Plea bargaining. Green river serial killer admitted to more killings (and cooperated to recover some of his victim’s bodies) in exchange for avoiding the death penalty : https://en.wikipedia.org/wiki/Gary_Ridgway#Plea_bargain,_con...

Crime gravity. If able to provide the solution to a crime that is considered more serious(or of greater value to the prosecuting entity's purview).

I doubt they admit to anything, but having some information that helps lead to the recovery of a valuable item could be worth something. To be honest, this is the first I have heard of the practice, but it sounds plausible to me.

"Hey, I don't have any idea how it got there, but I heard some guy talking about a famous stolen painting that's stashed right here in this neighborhood. Apparently a Renoir."