Celebrity impressions, when done right, can be hilariously entertaining. Just ask anyone who has seen Rich Little’s Las Vegas act over the years.

A new competition series debuting this week puts the spotlight on up-and-coming talent in that arena.

In “First Impressions With Dana Carvey,’’ premiering Tuesday at 10:30 p.m., on USA Network, amateur impressionists compete against each other in a series of challenges, with the winner determined by the studio audience. Along the way, they hone their impersonation skills with the help of in-house expert and Emmy winner Carvey (“Saturday Night Live,’’ “Wayne’s World’’) and celebrity guests, including Steve Carell (“The Office’’), Jay Leno (“The Tonight Show’’), Kevin Nealon (“Saturday Night Live’’), Yvette Nicole Brown (“Community’’) and Tom Arnold (“Sons of Anarchy’’). Freddie Prinze Jr. is the host of the half-hour series.

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During his seven seasons on “SNL,’’ Carvey made a name for himself imitating celebrities, among them Ross Perot, Woody Allen, Johnny Carson, Regis Philbin and one for which he is probably best known, former President George H.W. Bush. Those were all hilarious, and laughter, he says, should be the main goal of any celebrity impressionist.

“I guess because I’m in the comedy world, ‘Can you make it funny?’ is the number one thing,’’ Carvey says. “And I guess, there’s some expectation that you would sound like the person, but I do think total accuracy is sort of overrated. I would go more for some weird angle but it’s truthful and something that’s funny about it.’’

Prinze, the son of legendary comic Freddie Prinze, agrees.

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“When an impression is dead-on, it’s more scary than funny,’’ he says. “So it’s always better to lean on your sense of humor and then let the rest of it come out because you don’t want to freak people out with your impressions.’’

As for the talent level on the show, both men say it is top-notch, and Prinze notes that one young competitor even came away with a development deal with USA Network. And there is plenty of it to be tapped, judging by the proliferation of celebrity impression videos on YouTube and other websites, Carvey notes.

“If you go online or to these clubs,’’ Carvey says, “you’ll see all these people doing impressions. And there’s a kid in his bedroom with a camcorder and he does this amazing Tom Cruise. So if the show keeps going, more and more people out there who don’t have a platform for this kind of thing, if you’re not Jay Pharoah or Darrell Hammond on ‘SNL,’ where do you do it?”