Labour leadership contenders Andy Burnham and Liz Kendall have said they will change the party rules in order to make it easer for MPs to get rid of a failing leader.
In the first hustings since nominations closed earlier this week, Mr Burnham said it was the "biggest change" that the party needed to make.
In contrast, Yvette Cooper was on the only one of the four leadership hopefuls to insist the party already had the rules in place to get rid of a leader who was not up to the job.
The issue prompted one of the sharpest exchanges of the debate - staged by BBC2's Newsnight - with Ms Kendall insisting she would be prepared to resign if she thought she would not win the next general election.
"It has been too long since we won those major elections. There are some MPs who are talking about having a new process whereby if colleagues think you are not doing well enough you can go," she said.
"I have to go through that as a local Labour MP. We should have that for the Labour leadership too because above all we cannot put our values into practice unless we win."
Mr Burnham said that "of course" the party should have the opportunity to ditch the leader if they were seen to be failing.
"If anything, this is the biggest change that Labour needs to make. It's looked like it's been run by an elite. I will make that change," he said.
"The party comes first, always," he added, prompting Ms Kendall to shoot back: "The country comes first."
Left winger Jeremy Corbyn said that there should be regularly opportunities "every or two years" for the party to change leader.
In contrast, Ms Cooper insisted the party already had the rules "to do that kind of thing".
"The last people who should be deciding what are the rules for this leadership contest are the people who are standing in the leadership contest," she said.
Mr Burnham, seen as the unions' favourite, used the hustings - held in Nuneaton, one of the key target seats Labour failed to win at the general election - to insist that he did not want to ditch the legacy of Tony Blair.
"Tony was the prime minister that won three elections for Labour," the shadow health secretary said.
"But, he didn't get everything right so we have to learn from the mistakes of that government. But, he did a lot of things right and he spoke to people's wishes to get on in life.
Ms Kendall, the shadow health minister, who is the candidate most closely identified with the Blairite wing of the party, insisted she was "the Labour leader that the Tories fear".
She said it was essential that Labour showed it was committed to tackling the deficit if it wanted to regain power.
"Too many people didn't trust us on the economy or with their taxes," she said. "That is the basic test of competence for any party that wants to govern. We have to address that or we won't win in 2020."
Ms Kendall appeared to suggest that Mr Burnham and Ms Cooper, the shadow home secretary, had too much "baggage" as a result of their links to Mr Blair and Gordon Brown.
Ms Cooper retorted: "I think there is an advantage in having experience. I make no apology for having run a £100 billion department."
She said that she strongly believed the time had come for the Labour Party to elect a woman leader.
"For the Labour Party which has campaigned for women's equality for over a century, it would be fantastic for us to smash that final glass ceiling and elect a Labour woman leader of the party and a Labour woman prime minister as well," she said.
But she refused to be drawn on whether she would support Ms Kendall if she did not win, saying "I am not backing anybody else."
Mr Corbyn, seen as the outsider in the contest who only just scrapped onto the ballot paper, won many of the strongest rounds of applause from the studio audience - including when he said he had never been a supporter of New Labour.
"Why oh why oh why did Blair have to get so close to Bush that we ended up in an illegal war in Iraq?" he said.
"The party has a opportunity now to rediscover its principled roots, rediscover the issues of equality, rediscover the issues of public service."
There were further cheers when he mounted an impassioned defence of the contribution which immigrants had made to the country.
"If there hadn't been immigration to this country, what kind of health service would we have, what kind of transport system would we have, what kind of education system would we have? We would be in a much more difficult place," he said.