After 15 years in the NHL, there’s a part of Matt Cooke’s game that he’d like to lose: his reputation for the rough stuff.

With five suspensions levied by the league and other acts criticized over the course of his career, the left wing still has work to do with the image makeover. But the Minnesota Wild’s view of Cooke when the market opened was that he is a reliable penalty killer, shot blocker and third line scorer.

So Cooke signed a three-year, $7.5 million contract with Minnesota on Friday, the last and most startling move made by the Wild on a busy first day of free agency. They also traded forward Devin Setoguchi, let forwards Pierre-Marc Bouchard and Matt Cullen sign with other teams, signed defenseman Keith Ballard and re-signed defenseman Jared Spurgeon.

Cooke has long been one of the most-loathed opposing players among Wild fans, dating to his aggressive performance against them in the 2003 playoffs when he was with Vancouver. Cooke also found trouble for various hits in recent seasons with Pittsburgh.

“I’m sure there’s a lot of fans there who maybe aren’t fond of me and they remember when I played for Vancouver, but hopefully I can change their opinions rather quickly once I get there,” Cooke said on a conference call with reporters soon after his deal was done.

In 2011, Cooke received what amounted to a 17-game suspension for elbowing Rangers defenseman Ryan McDonagh in the head. Cooke was banned for the remainder of the regular season and the first round of the playoffs that spring. Sobered by the punishment, Cooke said he needed to change the way he plays.

“My actions will prove it,” he told reporters then.

Though that was his last suspension, Cooke’s style was questioned anew in February when his skate blade snapped the Achilles tendon of Senators defenseman Erik Karlsson. Cooke, who was not penalized or suspended for that, said he meant no harm.

“I’ve watched him play for many years. There’s no question when he came in the league he was an agitating player,” Wild general manager Chuck Fletcher said, adding: “With the new rules in our game, I think Matt has learned to not take every hit. You see him now passing up on some hits. He angles a lot. He’s always in good position defensively and yet he still has that physical presence.”

Cooke will make $1.5 million this season, $3 million in 2014-15 and $3 million in 2015-16.

He has a plus-53 goal-differential rating for his career. He hasn’t missed a game in either of the last two seasons. In 2011-12, his 38 points on 19 goals and 19 assists were the second most of his career. And his penalty minutes are way down. Since the hit on McDonagh, only three times in 151 games including the playoffs has he received more than four penalty minutes in a game. He took a major against the Bruins in the Eastern Conference finals last month for checking from behind.

He’s still a physical player, bringing the kind of grit the Wild wanted for their third line after trading Cal Clutterbuck. But, Cooke insisted, that grit isn’t dirty.

“There’s still times that you can go out and get a hit and get big hits that are clean, and they’re part of the game. It was the other ones that I wanted to get rid of,” Cooke said. “I still averaged over two hits a game this past season, and that’s something I want to keep in my game.”

The Wild are happy to have that.

“I just think Matt is, to be honest with you, an ideal third-line left winger. For our team right now, we’re in the process of learning how to win, of how to become a better team. Players like Matt bring different dimensions. But he has become a really good two-way hockey player,” Fletcher said.

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