Plaid Cymru delegates have called for police officers who covered up the truth behind the Hillsborough stadium disaster to be brought to justice.
An independent report has criticised South Yorkshire Police's conduct on the day and a subsequent cover-up into the deaths of 96 people in April 1989.
Plaid's Westminster leader Elfyn Llwyd said the affair calls into question the moral authority of the state.
The party also discussed the future of the UK on the conference's final day.
The motion on Hillsborough backed calls for the inquest verdict of accidental death of 96 Liverpool football fans at an FA Cup semi-final to be overturned.
Mr Llwyd said it was vital to "support every effort to turn this ugly truth into justice on behalf of the families".
He added that unless justice was done it would call into question the "moral authority of the state to govern".
Delegates also backed a motion calling for the voting age to reduced to sixteen in any future referendum on Welsh independence.
Mr Llwyd later repeated his calls for the criminal justice system to be devolved.
He told the conference: "As our means of policy shaping and law making develop and the Senedd grows in confidence, it stands to reason that the structure of our justice system should develop to encase it.
"It is remarkable to consider that Wales is the only country in the world that has a legislature, but no legal jurisdiction of its own."
The MP is also calling for powers over broadcasting to be devolved to the Welsh government and for the establishment of an "integrated Welsh Public Service encompassing the civil service, local government, and public services for the good of all public sector workers in Wales".
The conference also discussed the future of the UK, with Lord Elis-Thomas suggesting the union of Wales, England, Scotland and Northern Ireland has run its course.
Speaking in a panel discussion, the party's former leader said the UK was "on it's way out of history".
Lord Elis-Thomas, who briefly had the party whip withdrawn this summer, argued a European union of regions was the logical constitutional outcome.
The current leader Leanne Wood has promoted the concept of a new relationship between the nations of the UK.
Lord Elis-Thomas also advised party members that "our work is to encourage England to pursue self-determination".
Until the discussion there had been little debate on the constitution in Brecon, as Ms Wood's team used the conference to focus on the economy.
Earlier, Ms Wood spent the morning at an environmental scheme at Llangattock, near Crickhowell.
The project signs up households for discounts on installing green technologies including solar panels and heat pumps.
Ms Wood said it was exactly the sort of scheme she would like to see rolled out across Wales as part of the green New Deal she announced in her conference speech on Friday.
"If people can come together and decide to roll out a programme like this then the sky's the limit, they can achieve anything," she said.
"I think that the opportunity for creating jobs with this kind of scheme is great and I really can see no reason, as long as you've got people who are willing to do it, why this can't happen anywhere in Wales," she added.