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LeBron James worked Ray Allen hard for two years, urging the veteran guard to come to Miami any time he saw him.

It's easy to see why.

Allen already has been a major factor in his first playoff appearance with the Miami Heat, who are one win from closing out their first-round series against the Milwaukee Bucks. He led the Heat with 23 points in Thursday's 104-91 victory, setting the NBA's career playoff record for 3-pointers in the process. He was their second-highest scorer in Game 1, when he had 20 points, and is averaging almost 17 despite playing less than 30 minutes a game.

"He's a big boost for our team," James said. "I knew what he was able to do against me in the past, and I knew that threat could add another dimension to our team that we haven't had."

Game 4 is Sunday afternoon at the Bradley Center.

Allen is one of the purest shooters in NBA history, and few teams knew that better than the Heat. No one has made more 3s against Miami than Allen, and he played a big role in the Heat's epic playoff battles with the Boston Celtics. So it was natural that the Heat would want Allen when he was a free agent last summer.

Why Allen would want the Heat was a different story, however.

A charter member of Boston's "Big Three," Allen would have to be part the supporting cast in Miami, which has its own Big Three in James, Dwyane Wade and Chris Bosh. His playing time would be cut by at least 10 minutes, and coach Erik Spoelstra made it clear during his recruitment that he'd be coming off the bench in his 17th season, a role some say hastened his departure from Boston.

"If it was easy, more veteran players would do it. More veteran players would sign up and sacrifice to be part of something special," Spoelstra said Friday. "Most players of his resume are not willing to take on a lesser role and it's a significantly different role than he's accustomed to."

Yet the 37-year-old Allen signed up willingly. He even turned down more money from the Celtics to sign with the Heat.

"I said, 'If that's not something you can accept at this point, we understand,'" Spoelstra recalled. "He said, 'I just want to have an opportunity to have an impact on the team and in the fourth quarter. That's when I looked at him and said, 'Ray, we still have pain from the fourth-quarter 3s you hit.'"

Despite having only casual relationships with most of his teammates when he arrived in Miami, Allen settled in with the Heat easily and quickly.

For all of the big names on their roster — in addition to James, Wade and Bosh, the Heat have Chris Andersen, Mario Chalmers, Udonis Haslem, Mike Miller and Rashard Lewis — the Heat are a tight-knit bunch. They've all put individual goals aside in pursuit of a championship, and that's helped put everyone, from James to Norris Cole on somewhat equal footing.

"These guys, truly love each other," Allen said. "There's so much banter taking place and everybody's a victim, whether it's good or bad stuff. When we go play it translates. There's no animosity, no ego. We can go out there and play the best basketball that we can.

"It's been great," he added. "In 17 years, it's probably the one year that went by the quickest. I had so many fun moments from off-the-court things ... to traveling on the road. It was incredible that it went so fast, and that's a testament to how much fun I had personally."

But Allen was looking for more than a good time when he went to Miami. He has one ring from the NBA Championship he and the Celtics won in 2008, and he wants another before his career ends.

He's certainly doing his part in this first series.

Milwaukee had raced out to a 10-point lead early Thursday night, only to watch Allen whittle it back to 2 with three straight 3s. After the Heat turned a six-point deficit into a 10-point lead with a 23-7 run at the end of the third quarter, Allen finished the Bucks off with a 3 from deep in the corner.

"Ray's amazing," Larry Sanders marveled. "He's moving fast, he's scoring, he's shooting the ball. He's probably the best shooter to play the game and he's still out there doing it. It's amazing to see."

And it's exactly what James imagined when he was making all those sales pitches.

"We don't take him for granted," said Spoelstra, who refers to Allen as "Everyday Ray." ''We've been on the other end of it too many times. That's why we recruited him so hard because we've been on the other side of those fourth quarters where he made two, three or four to put you away."

Notes: Sanders said his right ankle, which he tweaked in a collision with Shane Battier in Game 2, was fine after playing almost 35 minutes Thursday night. ... Bucks coach Jim Boylan wasn't planning to use Samuel Dalembert during the playoffs, but he played nine minutes Thursday because Ekpe Udoh is struggling with an Achilles injury and Milwaukee needed someone on Chris Andersen. Asked if Dalembert would play again Sunday, Boylan said he'd have to see how Udoh is. "When he's right, he's really good for us. But in the situation we're in now, we have to throw everything out there."