The term "baby mustache" refers to light whiskers that are almost unnoticeable on the top lip of an adult male. According to Newsmax, Justin Bieber created a buzz when he appeared at New York Fashion Week sporting a baby mustache in 2013.
"The Pencil" is another name used for this type of facial hair on men. It "...is defined as a thin and narrow, closely-clipped moustache," as noted in men's magazine, Ask Men. Males with thin or slow-growing facial hair are best-suited for this type of mustache because it typically requires a good deal of upkeep to prevent it from becoming overgrown.