Participants with major depressive disorder and insomnia who meet all study criteria will receive state-of-the-art antidepressant medications and one of two insomnia therapies. The specific therapy for insomnia will be determined by chance (like a flip of a coin), with an equal chance to receive either cognitive-behavioral therapy for insomnia or desensitization psychotherapy for insomnia. The study physician will select an initial antidepressant medication from a list of three possible medications . If that medication is not helpful, another medication may be tried after 8 weeks or in the event of severe side effects.