CHICAGO — It is Saturday morning, and 10-year-old Henry Hailey is up at the crack of dawn. Still in PJs, his microphone-equipped headphones glowing blue in the dim basement, he fixates on the popular online game “Fortnite” on a large screen.

“What?! Right as I was about to finish it, I died,” he calls out disappointedly to his friend Gus, a fellow fifth-grader playing the game from his home just a few blocks away. “Dude, I should NOT have died.”

The digital battles resume, and Henry’s enthusiasm never wanes. Would he play all day if his parents let him? “Probably,” he concedes with a slight grin.

But they do not. Like many other parents, the Haileys are on a reinvigorated mission to limit screen time for Henry and his 15-year-old brother, Everett. For some parents, it feels like an exercise in futility. They are busy, overwhelmed and tired of the fight against increasingly omnipresent screens.

Getting Henry off screens has been a constant battle, his parents say. “Then once he’s off, there’s a lot of complaining and grumpiness for a while as we try to coax him to do something else,” says his mom, Barb Hailey. “He’s upset. Mom is a crank. What is it all for?”

The goal, experts say, should be to help kids learn to manage their own time as they get older and to stay physically active and socially connected as much offline as on. But parents in many American households are finding the power struggles — tantrums, withdrawal and, in some cases, even school and discipline problems — difficult, especially as more kids get access to screens at younger and younger ages.

A survey of 13- to 17-year-olds released this fall by the nonprofit Common Sense Media found that 95 percent of U.S. teens have their own mobile device. Seventy percent of them check social media several times a day, up from 34 percent in 2012. More than half say that their devices distract them from homework or the people they’re with.

Some tech companies now at least acknowledge concerns about over-use and outright abuse of digital media. Apple instituted a “Screen Time” function in its latest iPhone software. It monitors app use and allows users — or their parents — to establish limits. Google For Families and Google Play, found on Android phones, and various independent apps also allow parents to monitor and set some restrictions.

But those features aren’t enabled by default, so new limits can come as a shock to those on the receiving end.

That happened late this summer in the Hailey household on Chicago’s North Side after dad, Allen Hailey, began watching the amount of time elder son Everett was spending on Wi-Fi. The teen was clocking more than four hours a day on sports videos, games and chats with friends on social media.

“I don’t think he had any idea how much time he was spending online,” says the father, who decided to block both boys from Wi-Fi during certain hours. He tested it out one night without warning.

One minute, Everett was talking to a friend on social media. “Then it went out,” says the teen, who immediately complained aloud about the injustice of it all. Dad held firm and told him he needed to read a book or go outside to shoot hoops.

“I didn’t do anything wrong to deserve that,” Everett still insists. “If I get my work done, I think I should have my own time.”

Researchers who study these trends generally refrain from using the word “addiction” when it comes to screens, as it’s not an official diagnosis in the mental health world. But this summer, the World Health Organization added “gaming disorder” to its list of afflictions. That is gaming that severely interferes with relationships, school and work. The diagnosis is still under review by U.S. health authorities.

From Henry and Everett’s perspective, the real problem is that their parents seem stricter than most.

Like a lot of teens, Everett often uses multiple screens in the evening. He saved his own money to buy himself an older-model iPhone — “to fit in,” he says — and also uses a Chromebook laptop for homework. At his age, his mom says, his screen habits may be “a lost cause.”

But she keeps working on limits for Henry. Games are not allowed on weekdays. And he gets screen time only if all his homework is done.

The Haileys sheepishly note that Everett routinely multitasks in his room with one eye on the Chromebook and often the other on his phone. “I think we’re kind of wimps,” Barb Hailey says. Henry doesn’t have a phone — yet.

But phones and other screens are not allowed during meals — a limit both boys seem to appreciate. Everett says when they go out to eat, he happily leaves his phone in the car and marvels at the number of other families who are at the table with screens. “That just looks bad,” he says.

Some parents simply put off getting their kid a phone. Jacqui Koch, a college professor and mother in Wilmette, Illinois, had her sixth-grade daughter sign a pledge to wait until eighth grade for a smartphone — part of the national “Wait Until 8th “ movement. Her daughter didn’t put up much fuss, in part because mom has limited tech use for years.

The idea is that Wait Until 8th and events such as the National Day of Unplugging , an annual event in March, will make screen limits more socially acceptable and less like an adult-world imposition on kids.

Another key: Parents setting limits with their own devices.

When Allen Hailey is on his phone while watching a football game, Everett is quick to tell him that he’s on his phone too much. “He gets really mad,” Everett says.

When mom comes home, she says she tries to put down her phone, though it’s hard not to check emails for work. “Let me just check in,” she’ll say — and before long finds herself on Instagram and Facebook.

“You can go down the rabbit hole so easily,” Barb Hailey says. “Then you get it thrown back in your face.”

It’s not an easy balance to strike, but all the Haileys are trying. “We may not like it,” Everett says, as his little brother nods. “But we know it’s for the best.”