BOSTON — Before joining the Celtics for the 2007-08 season, Kevin Garnett and Ray Allen had accomplished just about everything they could in the NBA except for one thing — winning an NBA title.

At the time, Celtics captain Paul Pierce had never achieved that goal, either. But when the new Big Three was formed, Boston’s trio of All-Stars decided to put winning above individual glory.

And at the end of the season, their personal sacrifice paid off as the Celtics captured the NBA championship.

They hope to do the same thing next season.

Boston has added another All-Star for the coming season in Rasheed Wallace, and talented small forward Marquis Daniels has committed to play for Boston next year. With Kevin Garnett’s rehab ahead of schedule, everything seems to be falling into place for the Celtics to have another great season.

“Right now, I’m happy with the way our team is, and if the season started today I think we could win the championship with this team,” Pierce said.

With Rajon Rondo quickly developing into one of the top point guards in the NBA and Kendrick Perkins being a dominant force under the basket at the defensive end of the floor, one has to wonder whether the Celtics have too many talented players who could become disgruntled if they are not getting enough playing time or if they are not putting up All-Star statistics like some of them are capable of.

But that isn’t something the Celtics are worried about.

“They thought that the year we won it,” Pierce said. “I don’t think you could ever have too much talent.”

It is all about winning, Pierce said.

“With the type of unit that we have, the unselfishness out there with these guys, [individual statistics are] not going to matter,” Pierce said. “We are all out there to try to win ball games. Even if my minutes go down, I don’t really mind because it’s all about winning at the end of the day.”

Playing fewer minutes should benefit Boston’s All-Stars. Wallace will turn 35 in September. Allen turned 34 last Monday, and Garnett is 33. Pierce, meanwhile, will turn 32 in October. All of them have accumulated more than 30,500 regular-season minutes in their careers.

“We’ve got up-and-coming young players in Rondo, Perk and Big Baby [Davis], and then we’ve got the four veteran guys that have been proven NBA champions, so I think it’s a comforting feeling for all of us to know that they don’t have to do it on their own,” Celtics director of basketball operations Danny Ainge said earlier this month. “They just have to play their role, and I think that’s very attractive to every one of them.”

When the Celtics won the NBA title in 2008, nine players averaged more than 17 minutes per game by the end of the regular season, so Boston coach Doc Rivers knows how to keep everyone happy.

Pierce said he can’t wait to see the lineups that Rivers comes up with.

“I picture it every day,” he said. “When you get that type of lineup out there, you’re talking about arguably one of the best front lines in the NBA next year. You have to have bigs [size] to win in this game, and when you have them as talented as these two [Garnett and Wallace], you’re going to be like a kid in the candy store. If Rondo doesn’t lead the league in assists, I’ll probably be upset because he’ll have so many options out there.”

Boston’s winning ways are what persuaded Wallace to turn down a bigger contract and a potentially larger role with a different team to join the Celtics.

“The bottom line is just to win, so that pretty much persuaded me to come over here,” Wallace said.

Like Boston’s Big Three, Wallace said he is willing to do whatever Rivers asks of him, and if that means coming off the bench he will do that. He said he would rather score one point and have the Celtics win than score 100 points in a loss.

“The great thing about him is that Rasheed is also an unselfish player,” Pierce said. “You hear him saying that if he plays one minute, comes off the bench and scores one point, he won’t care as long as we win. That’s the kind of characteristics we have around our whole ball club…We just feel like it’s going to work because [we] don’t care about anything else but winning.”

The Celtics were one win away from advancing to the Eastern Conference finals last season. They got that far without Garnett (knee) and Leon Powe (knee).

There is no doubt in Pierce’s mind that the Celtics will go farther next season if they are healthy.

“On paper right now, it looks really good,” Pierce said. “We can be a better offensive team and defensive team. When you add Rasheed, he adds both pieces to the puzzle. Our main focus is going to be on defense, but offensively it’s going to be great.”