The Greens' dilemma about their future, in the words of one of the party's MPs, ''congealed'' in the wake of March's NSW election. Greens in that state, unofficially led by Rhiannon, found themselves mired in a damaging controversy over an Israel boycott enforced by a Greens-held local council. They also failed to convert legions of disaffected Labor voters. Cate Faehrmann, who replaced Rhiannon in the NSW upper house, called for ''necessary soul searching'' in an unusually public post-election critique of her own party in The Sydney Morning Herald. Later this month, Brown will address the National Press Club and is expected to unveil the portfolios for his new party room of 10: five existing senators and lower-house balance-of-power MP Adam Bandt, plus four new senators, including a first-time Victorian Greens senator, Richard Di Natale. Come July 1, Brown will command a taxpayer-funded staff of more than 50, a far cry from his parliamentary debut in 1996, when it was just him and a handful of staff. The only thing holding the party back, many senior Greens believe, is Rhiannon's old-school brand of leftist politics. And, as July 1 creeps closer, they are unnerved by her continued commitment to the anti-Israel Boycott, Divestment and Sanctions campaign, which is not Australian Greens policy and over which Brown has reprimanded the NSW Greens. ''I believe the Greens have huge potential for expansiveness, to carry the community along with really good policies and principles,'' said one senior party figure and long-term colleague of the senator-elect, who, like many The Sunday Age spoke to, would only talk on background. ''But Lee and her very close associates in NSW opt for a type of trench warfare and party-building that is very old-fashioned.''

For her part, Rhiannon - who remains much-loved and admired in the NSW Greens - denies there is any factional divide nationally but agrees there are differences of opinion. She rejects the notion that the Greens are ''just a protest party''. ''We have always been serious about contesting elections, as well as having that commitment to grass-roots democracy. One doesn't negate the other,'' she says. Lee Rhiannon is the only child of two significant Australian communists and activists, Bill and Freda Brown. Emotion overwhelms her when she talks about her parents, both of whom are now dead. They were, she says, two working-class people who wanted to make the world a better place, a goal that drives her. Growing up in Sydney's beachside Bronte, she lived with the Cold War as a backdrop and was surrounded by talk of politics. Because her parents were ''known communists'', Rhiannon boasts an ASIO file five volumes thick, the first entry written by government spies when she was just seven. Rhiannon would later join the pro-Soviet Socialist Party of Australia, even after the Soviet invasion of Czechoslovakia, which many Australian communists condemned. She is no longer a socialist. Now, as a Green, the qualified botanist wants more government regulation and a bigger role for public services such as education, health and transport, but not the overthrow of capitalism.

She has spent her life fighting for the environment, feminism and human rights, and her achievements are many: she was a founder of AID/WATCH, which grew into a significant watchdog on aid, an anti-Vietnam War and apartheid protester and she campaigned for gun control. On top of all this, she is a mother of three. When she and union official Paddy O'Gorman separated after 10 years, she decided not to keep his name and did not want to revert to her maiden name. Instead she asked her friends to suggest a surname. On top of the list was Rhiannon, which she chose not because of the Fleetwood Mac song or mythical Welsh goddesses. She just liked it, she says. Rhiannon was a formidable force during her decade in NSW's upper house, running many transparency and accountability campaigns that resulted in the stripping back of perks from superannuation to parliamentary catering. She also set up the ''Democracy for Sale'' campaign, which exposed Labor and Liberal links to the development industry and earned her some heavy-weight enemies. One senior Greens strategist says Rhiannon ''pushes hard on things that she believes in and she ends up having arguments and people don't like that. But I respect her for that … I really admire her commitment, tenacity and her passion, but sometimes she's really frustrated me because I've been on the other side of the argument.'' The consensus is that Rhiannon is quick to be combative, as The Sunday Age learnt while asking about her mother's frequent travels overseas for work. When this matter was raised, Rhiannon finished the question: ''Was she my mother? Was she there for me? You can cut to the chase. Totally, she was my mum … She was an ordinary woman who loved us absolutely.''

Two days later, Rhiannon called to say that she thought our question amounted to an assumption that women cannot work and be good mothers. She wanted to reject that assumption and its ''undertones of sexism''. She added: ''Coming from a young woman I just found it extraordinary.'' Rhiannon denies the suggestion that she is combative, saying she strives to build alliances. ''I certainly argue my case passionately but that doesn't mean I am combative,'' she says. Loading

It is much speculated upon in Canberra that Rhiannon's next big stoush will be to challenge Brown for the leadership. But not one person inside the party who The Sunday Age spoke to considers this a genuine possibility. For starters, Rhiannon herself has ruled it out. And then there's the commonly held view that, as one senior Greens MP puts it, ''Lee just does not have the support of the other senators … It's actually impossible and she knows it.''