Australian Open Tennis Day  11 , Li Na during her victory over Maria Sharapova on Rod Laver ArenaPhoto Pat Scala The AgeThursday the 24th of January 2013

Grace and power ... Li Na shows the strength of her ball striking during her quarter-final at the Australian Open this week. Photo: Pat Scala

THE technical improvement in Li Na's tennis has been with her serve and forehand; the bigger change in China's most famous sportswoman is a happy combination of heart, legs and mind.

When Justine Henin's former mentor, Carlos Rodriguez, started working with the 2011 French Open champion in Cincinnati in August, he began to view up close what he had long noted from the opposition coach's chair.

Rodriguez had seen a supreme athlete, one of the best in the women's game. A powerful ball-striker who could manage rallies but not her emotions, whose feelings - unlike the more insular, controlled Henin - were always on public show. The first Asian player to win a grand slam singles title and former world No.4 had failed to win another title or reach a grand slam quarter-final since her momentous Roland Garros breakthrough.

Had she under-achieved in her career, overall?

''No question about it, but I start to understand why,'' Rodriguez explained ahead of Saturday's Melbourne Park decider against top seed Victoria Azarenka. ''There is always a reason why a human being is not able to get the best from herself, and it's not a question of tennis.

''Now, there is many questions that she has started to answer herself: why [does] she play tennis? Why is [it] so important for her to be out there in the semi-finals? You have a pleasure, but when I saw her before, I don't see any sign of pleasure. Then why [do] you play? What satisfies you? And when you understand that, then you're able to really give the best of yourself.''

Li had several answers that satisfied the famously exacting Rodriguez, including the appeal of competition and the sense of self-worth and achievement that comes with success.

''The most important thing that I also help her to understand is that tennis today gives a very important sense to her life,'' he said. ''And I think she starts to understand how important for her that, as a person, she found something that allowed her to feel proud of herself, to feel fulfilled.''

The latest adjustment to the Li entourage has resulted in a change, too, for her husband of seven years and long-time coach and sparring partner, Jiang Shan, in the interests of domestic harmony and his wife's professional advancement. The practice court shouting matches are over, and Jiang claims to be happy in what is a different support role.

He is happy to let Rodriguez do the coaching, and is pleased with the results.

''I think Carlos have so many important things, new things for Li Na - [she] can hold herself [together] in important match, not up and down, up and down too much - can keep the same level all the match.''

About tennis, Li listens more to Rodriguez than she did to her husband. So, who is in charge at home? ''Who is the boss? Her, her - no question about it!''

The 30-year-old's authority on the court, too, was breathtaking against second seed Maria Sharapova on Thursday, in what Li, the world No.6, described as probably the finest match she has played.

Rodriguez is still not wholly satisfied with her serve, but has worked to bring more topspin to a rejigged forehand hit with a more open stance, and thus easier to execute on the run. Li's running forehands down the line were a feature of her semi-final domination.

''I hope that you see the match and you see how cool she was,'' Rodriguez said. ''I think that besides the technical things with the serve and the forehand she is more stable. I can change a lot of things but if you're not there with your state of mind - I say always to her 'do not fight against the environment or the things, just play, and try to enjoying yourself as best as you can'. The most important improvement today is how she manage the match in terms of emotions and mental[ly].''

In that regard, she is far different from Henin, who won seven grand slam titles from 12 finals, using her great variety and court craft to regularly outplay those bigger, stronger and more athletic. Li is five centimetres taller - ''her physical skills, I tell you, unbelievable,'' enthuses her new coach - but has had to learn to play not only with force, but with more margin and control.

Both his charges are ''very sensible'', but with Li outwardly more demonstrative, Rodriguez impresses on her the need to deal with her anger internally, exhale and try to stay calm.

That, he believes, will play a big part in Li's longevity, for she might be 30, but is younger in tennis years. Rodriguez admits he has to remind her she moves better than many far younger players, so the ageing issue does not become self-fulfilling. What he wants is what she managed so perfectly on Thursday. ''During the shots, she have to breathe and relax a little bit more, you don't feel the fatigue, because if you're like that [clenches his shoulders] after one hour you're exhausted.''

Li admits her body language was too revealing in the past.

There is now less of the stress and excitement that comes with her trail-blazing status in her homeland - Li quips she is ''maybe not so interesting'' now she owns one major title and is in a position to claim No.2 - and this has helped.

She insists there is also less pressure from within. ''So I come to the court, take the racquet, enjoy the tennis,'' she said.