MIAMI -- Once again, Gary Payton couldn't turn down Shaquille O'Neal. Payton signed a $1.1 million, one-year contract with the Miami Heat on Thursday -- a move that begins a reunion with O'Neal, who lured him to the Los Angeles Lakers two seasons ago for what ultimately was a failed title run. Now the duo is determined to get Payton -- a nine-time All-Star entering his 16th NBA season -- his first title. "We want to win basketball games, and not let our egos get in the way," said Payton, the latest big-name addition to join the Heat this offseason. "Everybody on this team has, at one point, been a star or a starter or a bigger part of their team. ... We have to understand that we are talking about wins, not who is going to have the points." Payton averaged 11.3 points and 6.1 assists for Boston last season, then became a free agent -- and O'Neal said he was "the only guy in the world" that could help Payton win a title. Apparently, Payton agreed. "We're very close, and when he steps up for me like that, it's hard to tell him no," said Payton, who played with Seattle in the 1996 Finals against Chicago, then returned to the title series with the Lakers two seasons ago -- losing both times. Miami will be Payton's fifth team, and he comes with career averages of 17.6 points, 7.2 assists and 2.0 steals. He's third on the NBA's all-time steals list (2,331), sixth in assists (8,508), 12th in minutes played (43,309) and 25th in points (20,829). Payton and Jason Williams -- another new addition -- will be the team's primary point guards entering training camp, which opens Oct. 4. "We are very fortunate to have been able to acquire a player of Gary Payton's stature," Heat president Pat Riley said. "He is a proven veteran and will be a big addition to this team." Miami lost starting point guard Damon Jones to Cleveland earlier this summer; Jones signed a four-year, $16.1 million free-agent deal. With Williams and Payton, the Heat believe they've improved markedly at the point over last year, when Keyon Dooling -- another free-agent departure, to Orlando -- backed up Damon Jones. Including playoffs, Payton has played in 1,315 games; he's started all but six of them. Yet he may be a reserve in Miami, something that he's apparently fine with. "I'm going to try to help Jason as much as possible," Payton said. "He has never had a guy like me to guide him. When I come into camp, I'm going to try to help him. I'm not going to try to beat him up or beat him down." Williams came to Miami along with forwards James Posey and Antoine Walker in a 13-player, five-team deal earlier this summer -- one where Miami gave up swingman Eddie Jones, another starter from the team that won 59 games last season and posted the Eastern Conference's best regular-season record. But that team fell short in the conference finals against Detroit, and Riley made major changes -- something that didn't necessarily surprise Payton. "Look at Pat. He's won championships and he knows what to do to get that extra oomph," Payton said. "Pat probably realized he didn't have that ... and he needed somebody who could make big plays at critical times." Payton said he doesn't expect this to be his final season, although he acknowledged that winning a championship could spark a change in that plan. He believes he could play as many as three more years, yet his sense of urgency to win a championship is stronger than ever. "We have a lot of new guys coming in that are going to have to learn the system," Payton said. "And we are going to have to get it together right away. I think that is where a lot of people are concerned about us. We have a good shot, we have a lot of talent here and we have to get cohesive very quickly."