Conservative leadership rivals David Davis and David Cameron have taken part in a live head-to-head debate in an attempt to win over the female vote.
Both candidates ruled out 'positive discrimination'
Speaking on BBC Radio 4's Woman's Hour, both said the party needed more than its current 17 women MPs, but ruled out "positive discrimination".
Mr Cameron said the party could "head hunt" good female candidates, but opposed all-female lists.
Mr Davis agreed on lists, but wanted more women in politics "at all levels".
The shadow culture secretary, Theresa May - who supports Mr Cameron - wants an "A-list" of 100 top Tory candidates, half of them female, to fight key target seats.
Mr Cameron agreed that any list should be "suggested", rather than a central demand on constituencies.
Mr Davis said it was important for local associations to maintain their "autonomy".
To attract more women voters, the party had to "stick to principles", while addressing issues such as education, childcare and healthcare.
Mr Cameron said the Conservatives had to "change our approach" to appeal to women, who were "not a minority".
The pair were also tackled about their attitudes to women and family.
Mr Davis denied he suffered from a "macho image" with female voters.
And he dismissed criticism of a party conference stunt involving young women wearing "It's DD for me" T-shirts, saying it was a "sense of humour failure" on his part.
Mr Cameron said he was a member of exclusive all-male gentleman's club White's because he went there to have lunch with his father.
"I don't think we have to be politically correct in every aspect of our life," he added.
He said he planned to take some paternity leave when his pregnant wife Samantha gave birth but he would be "flexible" about the timing of it.
The pair are making their appeals at a critical stage in the Tory leadership contest, with postal ballots landing on the doormats of 254,000 party members, who have until 5 December to vote.
Meanwhile, a Populus poll of Tory voters - rather than members - for the Times newspaper gives Mr Davis a lead over his rival.
The poll - of 122 Tory supporters - gives Mr Davis a 50% to 37% lead over Mr Cameron.
The contenders said they were enjoying the leadership race
Mr Cameron's team pointed out the Times poll also showed that, when Tory voters were asked who they thought most likely to win the next election, 45% said Mr Cameron, compared with 11% who said Mr Davis.
Mr Davis told Woman's Hour trends were going "in the right direction" and Mr Cameron said through a long campaign there would be "polls that made you happy and polls that made you less than happy".
Both candidates will give speeches and take questions at the Conservative Women's Conference in central London, later on Wednesday.
Mr Davis will talk about his challenge to make the party "the natural home for women voters".
Research published just after May's general election suggests that 50% of women who did not vote Conservative could not see themselves doing so in the future, he will say.
"So I find it simply incredible that we, as a party, do not make more use of your knowledge and expertise," he will continue.
"Let me be clear, I want women represented at every level of the party once again - at constituency level, at area level, at regional level and crucially, at board level too.
"That's why as leader, I will use one of my nominations to put a woman on the [Conservative Party] board.
"Without this level of involvement in every area of our party, we can't hope to build the best policies and the best campaigns to attract female voters back to the Conservative fold.
"This party should be the natural home for women voters. Our values, our belief in freedom, individual responsibility and giving people greater control of their lives should resonate with them."
Mr Cameron has said previously that "having more women standing for Parliament is not political correctness, it is political effectiveness".
"If the conversation we have within our own party doesn't reflect the conversation we're having with the general public, we won't win, and we won't deserve to win," he said.
* Earlier versions of this story incorrectly reported that the Davis/Cameron poll result was based on telephone interviews with 1,512 Conservative supporters, rather than the actual figure of 122.