BOSTON (AP) — Little 5-year-old Rashiyah Wallace sat on her daddy’s lap as he talked about joining the Celtics.

He laughed, smiled and joked. Not a single nasty word or stern look.

Fans who have watched Rasheed Wallace lose his cool and pick up technical fouls haven’t seen the lighter side of him very often.

“I will go off at times,” he said Thursday. “Overall, I’m a pretty good teammate.”

That’s one reason Celtics president of basketball operations Danny Ainge pursued Wallace, even calling his agent, Bill Strickland, just after midnight on July 1, the start of the free agency period.

“He’s completely different than how he’s perceived in the public,” Ainge said. “You can see how much our guys respect him.”

Wallace’s wife and two of his sons sat in the audience at his news conference after he signed a three-year contract with Boston after 5 1/2 seasons with the Detroit Pistons, where he won an NBA title in 2004. Now he’s part of the Celtics family. New teammates Kevin Garnett, Paul Pierce and Ray Allen beamed as they sat beside him.

“I know that we’re all looking at each other, feeling like teenagers again,” Garnett said.

Pierce thinks the addition of the 6-foot-11 Wallace’s rebounding, defense and outside shooting enhances the Celtics chances to recapture the NBA championship it won in 2008.

“Every day I try to envision it,” he said. “If it goes the way I envision it, it’s going to be a great summer next year.”

The Big Three talked in the locker room soon after their Game 7 loss to Orlando in the Eastern Conference semifinals and agreed on what the Celtics had to do – make Wallace their top free agent target.

“Rasheed was at the top of the list for all of us,” Allen said. “We even talked about it during the year because we knew he was going to be a free agent.”

They wanted him so badly that all three flew to Detroit to meet with him last week along with Ainge, coach Doc Rivers and owner Wyc Grousbeck. The presence of the players surprised Wallace. All three already knew him, so they discussed the team’s practice facility, schools in the area and other issues that might sway him.

“They clearly are pretty good salesmen,” Rivers said.

But Ainge believes the players’ visit didn’t tip the scales in Boston’s favor.

“I think it’s because of who these guys are on the court that Rasheed wanted to come here,” Ainge said.

Wallace also drew interest from San Antonio, Dallas, Orlando and Cleveland, with the Spurs emerging as the Celtics’ prime competition. But he felt Boston was “a good fit” and gave him the best chance to win his second championship.

He wants that so badly that he’s even willing to come off the bench after being a starter in his 14 previous seasons. For his career, he’s averaged 34 minutes, 15 points and 6.9 rebounds with 1.4 blocks.

“Two minutes, 30 minutes, whatever, as long as I’m contributing to the team for the ‘W,’ ” Wallace said. “If I score a point and we win, hey, it’s the sorriest point I’ve ever scored but we got the win. That beats 100 points and a loss any day.”

Wallace figures to get plenty of playing time as the backup to Garnett at power forward and Kendrick Perkins at center. Ainge wants to retain backup forward Glen Davis, a restricted free agent, and remains interested in free agent Grant Hill, although he could stay in Phoenix.

“We’re going to have to do more selling there,” Rivers said.

Wallace’s outside shooting gives opponents another player to double team and should open up shots for point guard Rajon Rondo, the weakest shooter in the starting lineup.

All that, plus a healthy Garnett, makes the Celtics a solid contender for another championship.

Garnett, who missed much of the second half of the season and all of the playoffs with a knee injury, said he’s ahead of schedule following surgery. Ainge expects him to be at full strength when the season begins.

When it does, Garnett will have another intense teammate. But who’s more intense?

“I would have to say I am,” Wallace said as his listeners laughed, “because he can control his emotions. Of course, everyone knows my history as far as technical fouls, but I don’t think you can match the intensity that I bring to the floor.”