Behavioral based interviewing has worked very well for me. The concept of BBI is that the best indicator of an applicant's future performance is his past behavior.
Basically, you determine ahead of time what are the qualities an employee must have in order to be successful at that position. You then ask questions that require the applicant to give specific examples of situations that have showcase that skill or quality.
Don't let them get away with being general. "I believe customers are number 1", doens't cut it. Ask for specific instances where their behavior has demonstrated that belief in action. Have them be as specific as possible, and then drill down and ask further questions based on the info they give you in their examples. This technique helps you to see throught the fluff and made up examples.
As far as making someone relaxed, my theory on that is I don't necessarily want them relaxed. I wanna see how they perform under pressure.
What position are you hiring for?