The tiny little body part people want plastic surgery on

It's a tiny body part, but for some, it can make a big difference during swimsuit season, say plastic surgeons who've seen an uptick in requests for belly button surgery.

New York City plastic surgeon Dr. Matthew Schulman said he's had more requests this year from women with "outies" who want an "innie" belly button.

Dr. David H. Song, president of the American Society of Plastic Surgeons and chief of plastic surgery at University of Chicago Medicine, agreed. "There's a lot of belly button surgery going on," he told CBS News.

"I do a fair amount if them. A lot of patients are paying way more attention to their belly buttons than ever before. People are getting more in shape and starting to pay attention to themselves. And showing off the midriff is in style," Song said.

The procedure is called umbilicoplasty and it's most popular with women.

"As a society we're becoming a lot more open to plastic surgery and a lot more aware of how we look," Schulman said. "There's a lot of social media influence. With the popularity of Instagram and Snapchat, our images are out there in the internet world forever and for everyone to see. It makes people more self-conscious and aware of their bodies."

He added, "I think people are starting to realize that there's actually something we can do for their belly button, that there's a solution."

The belly button is your first scar, where the umbilical cord -- which connects a fetus to a pregnant mother's womb -- detaches after birth and falls off, Song explained.

Whether you end up an innie or an outie is typically determined by genetics, though some medical experts say post-birth care of a baby's umbilical area may make a difference. For example, if it's cleaned in alcohol, the cord may dry up more completely and be more likely to leave an outie.

But sometimes people may become an outie later in life after getting pregnant or if a lot of weight is gained.

Dr. Scot Glasberg, a plastic surgeon in private practice in New York City and past president of the American Society of Plastic Surgeons, said an outie may be the result of an umbilical hernia, meaning some tissue from inside the abdomen has popped out and into the belly button.

"What I often see is a patient comes in with an outie and it's actually a small umbilical hernia," said Glasberg. "You go in and fix the hernia and then you tack it down to the tissues underneath to try to make it an innie. That's the most common scenario," he said.

Schulman said he also sees a lot of patients who want to correct old belly button piercings.

"Some women have old belly button piercings that they don't wear anymore and don't like the look of anymore, that they got back when Britney Spears wore one, and everybody was walking around with a midriff shirt and a belly button piercing. All those 17-year-old girls are now 32-year-old mothers. I'm doing a lot of those," he said.

"Belly button piercings look very strange later in life when you don't have a ring in it and you've had a baby. The piercing is higher than the belly button. It can end up an inch or two above the belly button," Schulman added.

Belly button surgery requests are particularly common in conjunction with a tummy tuck or a mini tummy tuck, plastic surgeons say.

"We see the age range in the post child-bearing years, in women anywhere between their late 20s and up to their 50s and 60s," Song said.

Song, who performs at least a dozen belly button surgeries a year without tummy tucks and about 20 to 30 with a tummy tuck, said it's important patients seek a board certified plastic surgeon.

He said to be sure the plastic surgeon is certified by the American Board of Plastic Surgeons, which is recognized by American Board of Medical Specialties.

A lot of people call themselves cosmetic surgeons, he warned, and may say they are certified, but he told CBS News, "There are a lot of boards not recognized by the American Board of Medical Specialties.

The cost of surgery runs the gamut depending on where you live, said Glasberg. New York, Beverly Hills, Dallas and Miami plastic surgeons tend to charge more. If a hernia is involved, insurance will likely cover the procedure, but if it's purely a cosmetic procedure, the price may range anywhere from $2,500 to $5,000. With a full tummy tuck, it may run in the ballpark from $8,000 to $12,000.

A straightforward umbilicoplasty can take an hour or two, and usually involves a local anesthetic. But a more involved abdominal surgery may take three or four hours in an outpatient surgery setting and require general anesthetic. Recovery time can range from a day or two to a couple of weeks.

Post-surgery, Song said, "I don't like to let my patients soak in water, like a pool or ocean, for at least three or four weeks because they do have an incision that needs to heal."

He says people thinking about belly button surgery for bikini season might want to plan for spring so they are healed up and able to swim by the time summer arrives.