Marcelo explains a critical yet oftentimes missed detail when finishing the Guillotine Choke. Your wrist must push into the neck. Don't pull your grip into the jaw. When on bottom, crunch up onto the back of the opponent's head and drive your forearm up into the throat; don't pull your arms away and extend your hip. When on top, e.g. the Mount, spread out your body and direct your weight into your grip -- once again, pushing the wrist into the neck and not pulling up on the jawbone. Lastly, if your opponent has a grip on your thumb, your chances of successfully finishing the technique drop dramatically. Try to hide your hands as much as possible. Expect that competitors may cheat and pull your fingers; this makes for good self-defense practice as well.