Police officers' promises of leniency are usually empty. Police officers may recommend a light sentence, but at the end of the day it's prosecutors and judges who normally determine punishment on the basis of statutory requirements and political expediency.
Case Example 1: Dee Nyal is arrested and charged with burglary. At the police station, Dee waives her Miranda rights and voluntarily tells the police that she is innocent, because she was at the movies at the time the burglary took place. At trial, the prosecutor wants to offer Dee's statement to the police into evidence to show it was false, because the movie Dee said she watched was not playing the night of the burglary. Dee protests that what she said to the police shouldn't be admissible because she didn't make a confession; instead she said she wasn't guilty.
Question: Is Dee's statement to the police admissible in evidence?
Answer: Yes. Dee waived her Miranda rights, so even though she was trying to help herself, the statement is admissible.
Case Example 2: Len Scap is arrested for murder. The police give Len his Miranda warning, then tell him that he might as well confess because the police found Len's fingerprints at the crime scene and because they have an eyewitness who can easily identify him. Feeling all is lost, Len confesses to the murder. It turns out that the police lied to Len—they had neither his fingerprints nor an eyewitness.
Question: Is Len's confession admissible in evidence?
Answer: Very probably. Judges generally rule that confessions are voluntary even if they are obtained by the police through trickery. （See Frazier v. Cupp, U.S. Sup. Ct. 1969.）