Carried out for Sir Tom Hunter's scotlandseptember18.com site by TNS BMRB, its headline result was Yes 32% (+2), No 46% (+4), Don't Know 22% (-6), as measured against a previous poll for Sir Tom.
The company has typically found more undecided voters than other polling organisations. Once they are stripped out, the Yes total stands at 41%, unchanged.
The poll also suggests voters may not be persuaded either way by the last phase of the campaign: 63% say they have stopped listening to the debate because 'both sides just contradict each other', while 73% say that it is hard to know which side to believe.
Professor John Curtice, in his What Scotland Thinks blog, says today: "The Yes side must have hoped that it would make further progress in reducing the No lead as and when undecided voters started to make up their mind.
"While there is little indication in this poll of any decline in Yes support, as suggested by the two most recent polls from YouGov, there is certainly no sign of any momentum. Of the seven polls TNS have conducted so far this year, all but one of them has put Yes on 41% (and the single exception was a reading of 40%).
"Not least of the reasons why the Yes side is apparently not making any further progress is that it is failing to make headway amongst those whose first preference is some form of devo max rather than independence or the status quo.
"Just 31% of voters claim to be aware that more powers are already on their way as a result of the 2012 Scotland Act...the poll goes on to suggest that in fact the No side might be able to extend its lead further if voters were more aware of the provisions of the Act, and especially so if they actually thought that there was a guarantee of more powers."
The poll confirms previous estimates that September 18 will see a high turn-out, with 75% saying they will definitely vote.
The TNS poll was conducted from June 10-23. Professor Curtice's poll of polls stands at Yes 43%, No 57%.
Commenting on the TNS findings, Sir Tom said: "This is an appalling state of affairs brought about by both sides of the debate, and this is an affront to our democracy.
"The future of our nation is rightly in the hands of our population, but that population is being enveloped by a thick fog of obfuscation."
Sarah-Jane Walls, operations manager for Yes Scotland, said: 'Support for Yes has increased since the last poll published by Sir Tom - it is over 40%, and we are confident of moving above 50% in the referendum.
"A key figure is that over two-thirds of people in Scotland want either the full powers of independence or devo-max, with the status quo a poor third.
"The reality is that none of the Westminster parties are offering anything like devo-max, therefore the only way to achieve these powers - so that we can make the wealth of Scotland work for all the people - is to vote Yes for independence."
Better Together campaign director Blair McDougall said: "This is yet another poll showing a strong majority for the campaign to keep Scotland in the UK.
"It's clear that the closer we get to the referendum people are starting to think seriously about the consequences of separation for our pound, pensions and public services.
"Scots want the facts about why being part of the UK is the best future for Scotland. We will do everything we can to make sure people get the facts they need. We are very confident that on the basis of the facts Scots will say No Thanks to separation."