Gary Leff, knower of all things frequent flyer, swears that his most important tip is this: Hang Up, Call Back (HUCB). When a customer service agent doesn’t give you the answer you want–or even the answer you know to be true–politely say goodbye, dial again and hope for better results in the next call. Gary suggests trying at least three times before giving up.

Truth be told, this tip always seemed a little unbelievable to me. Customer service agents were all on the same page (literally: the manual), I thought. But I had occasion to put the tip to use this weekend. And now I’m a believer.

I faced a simple task: Cancel one night on a three-night reservation at a Hilton.

Call #1: The agent looked a moment at my reservation, muttered, “Hmmm,” (never a good sign) and told me she’d need to speak to a supervisor. We were then cut off. Coincidence or bad luck? I think not.

Call #2: The agent told me Hilton could not alter the reservation because it was made through a convention housing service. She provided me the housing service’s 800 number. So helpful! Not. The recording informed me I had just won a cruise (if I would stay on the line). Clearly the wrong number. Which is when I remembered Gary’s advice.

Call #3: After the agent told me the same story about the housing service and gave me the 800#, which I knew to be the bogus cruise prize phone number, I protested. I politely explained why I believed Hilton was actually the party that should change the reservation. She put me on hold to talk to her supervisor and eventually came back to tell me the reservation had been changed. Eureka. Lesson learned: Thank you, Gary!