ISTANBUL—Turkey's economy is getting hairier, as a booming medical sector profits from a growth spurt: mustache transplants.

Long favored as a destination for the follicly challenged, Turkey's cosmetic surgeons have for years offered hair implants to those who are balding on top. Now hair transplants for the face are growing in popularity, cosmetic surgeons and tourism agencies say, with men from the Middle East, Europe and Asia coming to Istanbul seeking a virile addition for the upper lip.

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