Research by Ipsos Mori for BBC Scotland looked at attitudes to giving the Edinburgh parliament more powers.
Transferring full control over welfare benefits and complete power over income tax - which goes further than the proposals set out by the Smith Commission - were both in the top 10 in terms of support from the public.
But the idea of having another referendum on Scotland’s future in the UK in the next five years was ranked 19th out of 23, with voters apparently unsure over this.
It comes after Scottish First Minister and SNP leader Nicola Sturgeon refused to rule out staging a second independence vote after the 2016 Holyrood elections.
When questioned on the issue in the first Scottish leaders TV election debate of the campaign Ms Sturgeon said if the SNP won the General Election in Scotland next month this would not trigger another referendum.
But she added it was “another matter” whether a vote for her party in the 2016 Holyrood elections would bring about a second vote on independence.
Ms Sturgeon said: “This Westminster election is not a re-run of the referendum campaign, if you vote SNP in this election it doesn’t mean Scotland has another referendum, or becomes independent as a result.”
When asked about what could happen after the 2016 Scottish elections, she said: “That’s another matter.
“We will write that manifesto when we get there. I will fight one election at a time. I’m putting forward in a couple of weeks a manifesto for this election and I will decide the content of our next manifesto when we get there, and people can decide whether or not they vote for that.”
A referendum on the UK’s membership of the European Union (EU) was more popular with voters north of the border than another independence ballot, according to the Ipsos Mori poll.
More than 1,000 adults were questioned for the research, with pollsters asking them to give various issues a score of between one and 10, depending on how important these were to them.
A score of one meant a policy should not be implemented while 10 was taken to mean it should be put into action immediately.
The most popular policy was increasing the minimum wage for those aged over 21, which was given a score of 8.2.
Giving the Scottish Parliament power over all welfare benefits was eighth most popular, with a score of 7.1, while transferring full responsibility for income tax to Holyrood came 10th on the list at 6.8.
Holding another independence referendum by 2020 was given a score of 5.6, compared to 6.1 for a referendum on remaining in the EU.
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