Champions Heat believe they are stronger than ever MIAMI (Reuters) - When LeBron James was first introduced to Miami Heat fans, after his 2010 free agency move from Cleveland, he made a promise that was latched upon as being typical of the brash, bragging coming from South Florida. Talking about winning multiple championships, James famously said: "Not two, not three, not four, not five, not six, not seven," while Dwyane Wade and Chris Bosh, his partners in the 'Big Three' smiled with approval. With number one out of the way, after the Heat's triumph over the Oklahoma City Thunder last year, the team so much of America loves to hate now haves their sights set on a second. James has been busy ticking off items from his personal bucket list. This year, he won his first NBA championship, was crowned league and NBA finals Most Valuable Player and won a gold medal in the London Olympics and he believes his team has what it takes to repeat. We can be better than we were this past season...We have the potential to be a lot better. That is scary," he said as the Heat gathered in pre-season training. The most obvious way in which James is right is in the key area of three-point scoring, where Miami had struggled a little in the past two years, and president Pat Riley responded by going out and signing the best in the business. Ray Allen is the all-time leading three-point scorer and a 10-time All-Star who won a championship with Miami's Eastern Conference rivals, the Boston Celtics, in 2008. Although Allen is 37-years-old and has had some injury worries, Riley hopes the Heat can get a couple of good seasons - and championships - out of him. "We have added one of the most professional professionals this league has ever seen," said Riley. He's part of new generation of athletes that may have become better athletes after 30. Even if Allen can't be on court as much as he would like, Miami have other options with a second free agent addition, Rashard Lewis. Lewis is a 14-year NBA veteran and two-time NBA All Star who played with Allen at the Seattle Supersonics from 2003-07. In their final season together they averaged a combined 48.8 points. After two injury-hampered seasons, Lewis will be hoping to have a shot at a maiden NBA championship. Riley said those free-agency acquisitions were proof of a determination not to repeat what happened after the Heat's 2006 title, when Miami failed to build on their championship. That was my mistake. You have got to keep adding pieces to it. We've got to raise the bar and expect more from ourselves," said Riley. The 'Big Three', with Wade, coming back from arthroscopic knee surgery in July, remain intact and the core of 'Little 12', as forward Udonis Haslem has dubbed the rest of the roster, is largely unchanged. Haslem, Joel Anthony, Shane Battier, Mario Chalmers, James Jones and Mike Miller can all expect plenty of minutes while more may be asked of point guard Norris Cole in his second year. Coach Erik Spoelstra has no illusions about how tough it will be to clinch a successive title. Everybody will be gunning for us this year. Teams have loaded up. They're primed and ready to take on the champions. It's a different challenge for us this year. It's a cliche to say it's harder to win the second time. It's just difficult. You have to commit fully, reinvest into the team. We think we've improved in the off season.