Vince Cable has completely rejected the idea of a pure graduate tax as a solution to student finance and university funding in England.
The Liberal Democrat business secretary, speaking during a fringe event at the party's annual conference in Liverpool, said he accepted that the idea "really doesn't work".
However, Mr Cable said the "essence" of the idea - that graduate payments be linked to earnings - was a "red line" for him in negotiations with his Conservative partners in government.
"The one strong commitment I have made, and this is a red line, is that the system that emerges has to be progressive," he told the meeting organised by the party's youth wing.
Of a pure graduate tax, he said: "It has a certain appeal on equity grounds. We have looked very hard at this in its pure form, and it really doesn't work for a variety of reasons."
In July, the minister sparked a fierce public debate about the possibility of a graduate tax when he said he wanted to see a system of variable graduate contributions tied to earnings.
His latest comments come just three weeks before the independent review of higher education funding and student finance, led by Lord Browne of Madingley, publishes its proposals.
There has been widespread speculation that the review will recommend keeping the tuition fee system and raising the cap, currently set at £3,290 a year. Such a move would be endorsed by research-intensive universities.
However, Mr Cable and other senior Lib Dems repeatedly said at the conference that the government could reject Lord Browne's recommendations.
"It is a high-powered group," Mr Cable said. "I am sure they will come up with sensible suggestions but we are not obliged to accept them."
Simon Hughes, the Lib Dem deputy leader, went a step further and said it was his "belief, hope and conviction" that tuition fees would be abolished after the government had carefully digested the report.
He told another fringe meeting that Mr Cable had been doing "sterling work" convincing civil servants that the abolition of fees was necessary to meet the party's pre-election commitment.
Almost all Lib Dem MPs signed a pledge before the election to oppose any rise in fees put to a vote in Parliament. However, the coalition agreement with the Conservatives only allows them to abstain.
Exactly what kind of system the Lib Dems would accept - and whether they would be happy for universities to influence the level of any graduate contribution - is still unclear.
Some MPs vehemently opposed to fees, such as Sir Menzies Campbell, have indicated that they will accept higher payments from individuals than at present if the system is progressive.
Although the issue was hardly discussed in the main hall of the conference, party members did vote to look at building support for a graduate tax.
A line in a policy motion on fairness asks the party to "explore the possibility of building cross-party support around replacing tuition fees and student loans with a graduate tax system".
A separate vote was held to try to remove the line from the motion because some members expressed concern that it was "rushing" towards a position before Lord Browne's report. However, this was defeated.
That leaves the party with a policy motion to consider a graduate tax - just days after one of its ministers went on record to rule it out.