CHICAGO – Johnny Oduya could have tested the free-agent market this summer.

Instead, the veteran NHL defenseman decided to stick with a sure thing.

“I had a good feeling in Chicago,” Oduya said.

The Blackhawks apparently felt the same way. They re-signed Oduya to a three-year contract Tuesday in addition to re-signing forward Jamal Mayers to a one-year deal.

Hawks general manager Stan Bowman said the deals were the first part of the team’s offseason plan after back-to-back first-round playoff exits. The league’s free agency signing period begins July 1, while the annual NHL Entry Draft will take place one week earlier and often leads to trade possibilities.

“We’re still going to look at making additional changes to our team,” Bowman said during a conference call. “You never know how that’s going to shake out.”

Oduya, 30, reportedly took a small pay cut to remain with the Hawks. His deal is worth a little more than $10 million, or $3.375 million a season for three years, according to TSN. Mayers’ one-year contract reportedly is worth $600,000.

As a puck-moving defenseman, Oduya fit in nicely after he joined the Hawks via trade Feb. 27. The Hawks acquired him from the Winnipeg Jets in exchange for second- and third-round selections in the 2013 NHL Entry Draft.

In 18 regular-season games with the Hawks, Oduya scored five points (1 G, 4 A) and had a plus-3 rating while averaging more than 24 minutes of ice time a game. He added three assists and a plus-1 rating in six playoff games against Phoenix.

“We brought Johnny in to try to solidify things down the stretch, and I think he played a big role in the turnaround of our team,” Bowman said. “I think it was pretty evident that his style of hockey complemented our style.”

Mayers, 37, proved to be a reliable fourth-line forward in his first season with the Hawks and his 14th season overall. He scored 15 points (6 G, 9 A) and led the team with 91 penalty minutes while averaging about 10 minutes a game in 81 contests.

Hawks coach Joel Quenneville benched Mayers after three playoff games in an attempt to spark the team. Mayers, who is a veteran of 63 postseason games, never complained about the move and said it did not dissuade him from returning.

“It’s tough as a competitor,” Mayers said. “But when you take a step back and take a look at the whole year, I think it was a good fit both for myself and the Hawks.”

Hawks bits: Bowman made his first public comments about a recent controversy involving forward Patrick Kane, whose wild weekend in Madison, Wis., was highly publicized on the Internet. “We’re obviously disappointed with how it played out,” Bowman said, “and Patrick’s aware of that fact.” … The Hawks agreed to three-year contracts with four prospects Tuesday. They signed forward Joakim Nordstrom, defenseman Klas Dahlbeck, goaltender Mac Carruth and goaltender Kent Simpson.