They can't do 2. Or at least it would make the confession inadmissible evidence. The case law for this goes back more than a century. The general rule is that the police cannot promise you anything in return for a confession.

> Bram v. United States, 168 U.S. 532 (1897), was a United States Supreme Court case that ruled that an alleged confession to a crime, in order to be admissible, must not be obtained by threats or violence, nor by any direct or implied promises, however slight.

https://en.wikipedia.org/wiki/Bram_v._United_States

The ruling was later applied to the states as well in Malloy v. Hogan

> The Court held that the Fifth Amendment's exception from compulsory self-incrimination is protected by the Fourteenth Amendment against abridgement by a state. When determining if state officers properly obtained a confession, one must focus on whether the statements were made freely and voluntarily without any direct or implied promises or improper influence.

https://www.oyez.org/cases/1963/110

The "you will get X years instead of Y years" has repeatedly been found to make testimony inadmissible. You might be confusing it with plea bargains which are legal but don't involve the police and are actually binding agreements. The prosecutor cannot lie to you about what you will receive in return for your cooperation.

> The general rule is that the police cannot promise you anything in return for a confession.

Yet plea bargaining is basically a promise in exchange for a confession (guilty plea), and that's why it's not allowed basically anywhere except the US.