The Wild struck with two signings soon after NHL free agency opened Sunday, but they weren't the "Big Two" Wild fans are craving.

As the Wild built up the depth of its third and fourth lines with speedster Torrey Mitchell and tough hombre Zenon Konopka, New Jersey Devils captain Zach Parise and Nashville Predators blue-chip defenseman Ryan Suter were flooded with multimillion-dollar contract offers from the Wild and several others.

So overwhelmed, Parise and Suter delayed making decisions until likely Monday.

Agent Wade Arnott said Parise has "narrowed the list of teams to a small select group," while Suter's agent, Neil Sheehy, said, "We have much to consider."

Late Sunday, as several teams were informed they were out of the running, General Manager Chuck Fletcher was informed that the Wild was on each player's short list, sources said.

Fletcher declined to discuss details about his conversations with both camps, saying, "We'll just wait and see how things play out."

For Parise, the Wild is believed to be head-to-head against Pittsburgh, Philadelphia and Detroit. For Suter, Detroit and Nashville are believed to be the Wild's biggest competition.

The Wild signed Mitchell, 27, who spent four seasons with San Jose, to a three-year, $5.7 million contract and envisions him as its third-line right winger. It signed Konopka, 31, who has 92 career fights and led the NHL in penalty minutes in 2009-10 and 2010-11, to a two-year, $1.85 million deal. The Wild envisions the enforcer/faceoff specialist as its fourth-line center.

"We have some other needs, but I don't think it can be understated how important it is to have quality guys on your third and fourth line ... to make you a better all-around team," Fletcher said. "Both these players make us harder to play against."

Seconds after free agency began, the Wild submitted lucrative contract offers to Parise and Suter. Fletcher, owner Craig Leipold and coach Mike Yeo planned to fly to Toronto to meet with Parise, but his agency soon cancelled all in-person visits.

The Wild brass made a presentation to the Minneapolis-born Parise by phone. For Minnesota, landing Parise, who has averaged .82 points per game in his career and ranks fourth on the Devils all-time list with 194 goals, is considered paramount to landing Suter, fourth on the Predators' all-time list with 200 assists.

If the Wild misses on Parise, it very well could miss on Suter.

Both could alter the fortunes of a franchise that has missed the playoffs four years in a row, which is why the Wild offered dramatically front-loaded, extremely lengthy deals. The Wild wouldn't discuss specifics of its offers in fear of disclosing secrets to its competition.

Mitchell, 27, who attended the University of Vermont, is a natural center who has played wing since missing the 2008-09 season because of a broken tibia. He has scored 73 points in 280 games.

He was "pumped" to sign with the Wild and be reunited with former Sharks teammates Dany Heatley and Devin Setoguchi.

"First thing [with Mitchell] is his speed," Heatley said from his home in Kelowna, British Columbia. "He's one of the top guys in the league; that's how fast he is. Real good team guy, a guy that's going to kill penalties for us, hound the puck. He's real tough to play against because of his speed and his tenacity."

Mitchell and Setoguchi lived together for three years in San Jose but won't do the same in Minnesota. "I'm getting married in two weeks, so that'd be kind of awkward," Mitchell said, laughing.

Mitchell is the player who broke Kurtis Foster's left femur after hitting the former Wild defenseman from behind on an icing in 2008.

"Not a good situation to be involved in," Mitchell said. "I'm glad he's recovered and the little trauma I had from it, I'm recovered. It was my rookie year and I'm a pretty honest player, and to get tangled up in that situation was not something I wanted to be a part of. It was difficult."

Konopka fought 18 times last season and has 765 penalty minutes since 2009-10, most in the NHL.

"[Mikko] Koivu is a superstar that maybe doesn't get enough respect around the league, and he should," Konopka said. "Heatley is a world-class player, and we have to make sure those guys are taken care of and they feel very comfortable and nice.

"If they want to sit down at center ice and read the paper, they should be able to do that without anyone touching them."

Unlike many fighters, Konopka can play a regular shift. He's a strong penalty killer, has a career .588 faceoff winning percentage and has 27 points in 250 games with five teams.

"I take pride in that kind of stuff," he said.

Adding Mitchell and Konopka could close the door for some Wild prospects in training camp, but Fletcher said, "I don't think we ever had any intention playing young players on the fourth line unless we're forced into it."