More devolution is the most popular option for the future of Scotland, according to new research.
So-called devo max - the devolving of all powers to Holyrood other than defence and foreign affairs - was favoured by 32% of respondents to the Scottish Social Attitudes Survey.
Independence was favoured by 31% of those surveyed, while 25% wanted the status quo.
Devo max is not an option for voters in the forthcoming referendum.
The ScotCen research also found that support for devo max rises to around two thirds when respondents were asked to choose between it and either independence or the status quo.
Researchers interviewed 1,497 adults between June and October 2013 for the survey.
On 18 September, voters in Scotland will be asked the straight Yes/No question: "Should Scotland be an independent country?"
Both Labour and the Conservatives have set up commissions to look at further powers for Holyrood, with both due to report before the referendum.
Last week, Scottish Conservative leader Ruth Davidson ruled out all three pro-Union parties reaching a joint agreement before the referendum.
Sir Menzies Campbell set out the Liberal Democrats' support for more devolution in a report titled Federalism - the best future for Scotland.
Professor John Curtice, a researcher with ScotCen, said the results of the survey showed that further debate on the merits of devo max was needed.
He added: "Doubtless supporters of the idea will note its apparent widespread popularity, while sceptics will point to the relative lack of enthusiasm for some of its consequences.
"But given that as many as 44% of those whose first preference is devo max have yet to decide how to vote in September, working out the best way of appealing to their sometimes seemingly inconsistent feelings and aspirations could well prove vital in determining the eventual referendum outcome."
Blair Jenkins chief executive of Yes Scotland, said independence was the only way to guarantee more powers for Holyrood.
He added: "Given that the Westminster government refused to offer a more powers question on the referendum ballot paper, it is becoming clear to increasing numbers of people that only a 'Yes' vote can secure powers over vital areas such as welfare, pensions and tax.
"Given the likely position of limited new powers and no guarantees, we fully expect more and more people who want more powers to choose full powers with a 'Yes'."
A spokesman for the pro-Union Better Together campaign said the poll showed devolution was "the settled will of the Scottish people".
He added: "We can have our own Scottish Parliament and we can have the strength and security of having the pound and being part of the UK. Only the nationalists think that we have to choose between the two.
"The Scottish Parliament is guaranteed significant new powers over the next couple of years through the already agreed Scotland Act. The three main parties are also discussing what other powers can be devolved to Holyrood and voters will find out about these in advance of the referendum."