A referendum on turning the Welsh assembly into a Scottish-style parliament would be too close to call, an opinion poll for BBC Wales suggests.
Power would shift to the Senedd if a referendum backed more powers
Asked how they would vote on whether to create a fully law-making Welsh parliament, 49% were for, 42% against and 9% said they were undecided.
It indicates how difficult it might be for First Minister Rhodri Morgan to call and win a referendum.
In a similar BBC Wales poll last June, 47% were in favour, and 44% opposed.
Retired diplomat Sir Emyr Jones Parry is chairing a commission paving the way to a referendum, which was part of the deal which led to the Labour-Plaid Cymru coalition assembly government after last year's election.
BBC WALES POLL
If there were a referendum on turning the assembly into a law-making parliament, how would you vote? 49% for; 42% against; 9% undecided
Which level of government do you think has most influence over Wales? Ass govt: 40%; UK govt: 35%; Local councils: 10%; EU: 8%
Which level of government do you think should have most influence over Wales? Ass govt: 61%; UK govt: 22%; Local councils: 11%; EU: 2%
ICM Research interviewed a random sample of 1,210 Welsh adults aged 18+ by telephone on 22-24 February. Interviews were conducted across Wales and the results have been weighted to the profile of all adults.
In a second question, voters were given a list of preferred options for the assembly.
A total of 37% said they wanted a Welsh parliament with law-making and taxation powers; 20% backed assembly abolition and 26% wanted things to remain as they are, with the assembly having limited law-making powers.
Some 8% wanted Wales independent of the UK but in the European Union, and 5% backed Wales independent of both the UK and EU.
The poll indicated there may be other signs of a changing mood among voters.
Previously, polls have suggested a majority of people believed the UK Government had most influence over Wales - although most believed the Welsh Assembly Government should have.
In this ICM poll, for the first time, more people said they believed the assembly government had more influence over Wales than its UK counterpart.
Almost one in four knows there is a Labour/Plaid coalition government
Some 40% thought the assembly government had most influence over Wales, while 35 per cent believed it was the UK government.
When asked "which level of government do you think should have most influence over Wales?" 61 per cent said it should be the assembly government, while only 22 per cent said the UK.
Overall, 65% of those questioned knew Labour was in power in Wales, while 47% knew Plaid Cymru were.
A total of 39% also knew that the assembly government was run by a Labour/Plaid coalition.
With local council elections now only weeks away Wales' 22 councils may be disappointed that only 10% of those questioned thought that local government had most influence in Wales, with 11% thinking they should have most influence.
Those questioned were also asked which issues will be most important to them when it comes to deciding which political party to back.
"Community safety and policing" as well as "delivery of social services, including care for the elderly" came top.
Least important was loyalty to a political party or individual candidate, which may suggest that it will be all to play for on 1 May.
Labour First Minister Rhodri Morgan said there was not much movement in support for a Welsh parliament, but "at least it is moving in the right direction" and he expected it would become "much greater".
Plaid Cymru's Helen Mary Jones said: "It is positive and it shows things are moving in the right direction, with a majority of those polled wanting a proper parliament".
Welsh Conservative leader Nick Bourne said there was a "substantial body of opinion" that wanted more powers for the assembly, adding: "It is also interesting that 60% do not seem to know that Labour and Plaid Cymru are in government, so it just shows they are not having much of an impact".
Welsh Liberal Democrat leader Mike German said: "This poll confirms that the case for a Scottish-style parliament is slowly but surely gaining in acceptance - even among the sceptical. It isn't clear cut, but the momentum is with those of us who want to go forward with devolution".