Sometimes you just have to tell the bad guy exactly what he wants to know. Or at least lie about it while it looks like you're doing so. Or give them too much information, so they become confused and unable to act. No need to risk your skin by holding out when the alternatives can be so much more entertaining.
Boba Fett: You must hand Solo over to me. He knows where Obi-Wan Kenobi is.
Darth Vader: He won't talk.
Boba Fett: I'll take him to a place where his brain can be sliced into molecule-thick layers and read out.
Boba Fett: And then I'll do the same to anyone you've ever cared about. I will have my vengeance.
Han: I'll tell! I'll tell!
Boba Fett: I knew you'd come around.
Han: He's me.
Han: I am Obi-Wan Kenobi.
Boba Fett: No! That's not true! That's impossible!
Chewbacca: Actually, old chap, I think you'll find it is I who am Obi-Wan Kenobi.
Leia: Wait! No! I'm Obi-Wan Kenobi!
C-3PO: I'm not!