It depends how sensitive your taste buds are. For me, a good standard cleaning would probably do it. A few smokes and it would be good, or maybe right away. But if you really hate any slight afterglow of Latakia, extend the cleaning until you feel comfortable. How much did you smoke the pipe? Less smoking takes less cleaning.
I only smoked it around once or twice a week, so it really didn't take that much effort at all to get everything out.