Among those who plan to vote No, 80% said they wanted a more upbeat approach, a Panelbase survey commissioned by the Yes campaign found.
The Panelbase poll asked if voters would like to see Better Together put a more positive case for the UK: 66% said yes, 18% said no, with 16% undecided.
Meanwhile, the lead held by the Better Together campaign for a No vote in September has shrunk from 19% in September to 12% in the latest survey, according to pollsters TNS.
The poll of 988 people found the No vote has dropped one point to 41% compared with 29% for independence, which is up one point from February. The other 30% were undecided or wouldn't give a preference.
Among those certain to vote, 33% will back independence, up one point, compared with 46% of people who say they will vote against independence.
The number of people who say they are certain to vote has increased to a high of 74%, up from 65% in September.
Tom Costley, head of TNS Scotland, said: "The increase in the proportion who claim they are certain to vote is an indication that more and more people are realising the importance of this referendum and are becoming increasingly engaged in the process.
"This survey shows that while many voters are now committed to one side or the other, a significant proportion of voters still have to make up their minds. Many undecided voters are telling us that they will definitely cast their vote, and how the campaigns address their interests is likely to have a big influence on the final outcome."
Blair Jenkins, chief executive of Yes Scotland, said: "This is another positive poll with a swing to Yes which follows the trend of the last six months - that of a continuous narrowing of the gap between Yes and No.
"The sampling for TNS, of course, was prior to that of three most recent polls - two for Panelbase and one for Survation - that had a stronger showing for independence with an upward trajectory for a Yes vote.
"We still have a lot of hard work to do to convince more people that Yes is the right choice for them, their families and for Scotland, but this poll is further evidence that we are moving steadily in the right direction."
A Better Together spokesman said: "It is encouraging that the campaign for Scotland to remain in the UK retains such a strong lead.
"There can be no complacency from those who believe the brightest future for Scotland is to stay in the UK.
"We will be doing everything we can between now and the referendum to make the positive case that we can have the best of both worlds as part of the UK."