Maybe most impressive about his debut season: He was only a teenager.
The 6-foot-5, 305-pound Tunsil just turned 20 last week, but the sophomore is undeniably one of the Rebels' most important players as they try to compete in the SEC's Western Division.
The Lake City, Florida, native was so good, so fast that his name is already appearing at the top of NFL mock drafts for 2016. But Tunsil — who is described as soft-spoken and uncommonly mature by teammates and coaches — brushes aside most compliments.
"I just don't pay attention to that stuff," Tunsil said. "I keep working and I stay humble. I've still got a lot of things to work on."
Tunsil was one of the prized prospects from the Rebels' 2013 recruiting class that also included defensive tackle Robert Nkemdiche and receiver Laquon Treadwell. He became a vital contributor almost immediately and was charged with protecting quarterback Bo Wallace's blind side.
Tunsil's importance was readily apparent late in the season when he left the Egg Bowl in the first half with a knee injury. Without him, the Rebels couldn't move the ball and eventually lost 17-10 to Mississippi State in overtime.
Ole Miss guard Justin Bell said Tunsil has an ideal mix of talent and maturity.
"Laremy was coached really well in high school because he came in and knew what to do immediately," Bell said. "And then part of it is just natural ability. He has great bending, footwork. He's just a natural talent — that's what he does."
Ole Miss returns a veteran team this season, which is one big reason the Rebels expect to improve on last season's 8-5 record.
But for coach Hugh Freeze, the offensive line is a concern. The Rebels are replacing three starters and the heir apparent at right tackle — sophomore Austin Golson — surprisingly elected to transfer during the spring.
That's why Tunsil's presence at left tackle is so soothing. It is one spot Freeze doesn't have to worry about.
"Obviously we have a special one in Laremy Tunsil," Freeze said. "We hope and pray that he has a healthy and outstanding year."
Tunsil said veterans like Bell were a big reason he had such a successful freshman season. He said Bell's advice was simple — "just keep your head on straight, learn from experience and keep your cool."
The Rebels open the season Aug. 28 against Boise State in Atlanta.
"You're not going to have to worry about us," Bell said. "We take pride in what we do. We're going to work hard this camp and we're using any negative criticism as motivation."