> I guess the lesson there is that if you don't want to be convicted of a crime, don't confess to a crime? They won't give you a lighter sentence for confessing.

Ever hear of moral integrity?

Unless the penalty is unjust (say, execution for a minor crime), a just man will confess and accept his punishment as right as just. He himself will want justice to be done and will want to pay for his crime.

A remorseful murderer knows he deserves death. He might ask for mercy, but failing that, he will accept the penalty with dignity and grace.