With five weeks to go before a crucial ballot on extending the free movement of people to new European Union members, a "yes" vote seems likely.
A poll by the GfS institute, commissioned by the Swiss Broadcasting Corporation, found 49 per cent of Swiss voters in favour of extending the EU accord and 36 per cent against.
The penultimate survey before the September 25 vote shows support up six percentage points compared with a poll conducted in July.
Opponents lost four percentage points over the same period, while the number of undecided voters dropped from 17 per cent to 15 per cent, according to the poll published on Friday.
About half of those interviewed (49 per cent) said they would definitely go to the polls next month.
Extending the accord will open the Swiss labour market to workers mainly from eastern Europe.
Claude Longchamps, who heads the Bern-based GfS institute, said one reason for the increased support was that debate had become more focused over the past weeks and potential voters had begun to weigh the pros and cons in a less emotional way.
A first poll last month came in the wake of controversial statements from a senior official in Brussels.
The EU foreign affairs commissioner, Benita Ferrero-Waldner, said the Swiss had to approve the labour accord if they wanted to be part of the passport-free zone.
In June the Swiss electorate approved the Schengen/Dublin accords on closer security and asylum cooperation with the EU.
"The comments caused considerable irritation and a public outcry," Longchamps told swissinfo. "But the indignation appears to have died down."
He added that another reason quoted by supporters was that the accord offers new job opportunities for Swiss in the ten new EU countries.
But many people are still concerned that an influx of cheap labour could push down salary levels in Switzerland.
The survey found a particularly high approval rate for the labour accord among voters of the centre-left Social Democrats (74 per cent) and in the French-speaking part of the country (56 per cent).
Two out of three supporters of the rightwing Swiss People's Party came out against the accord and opposition appears to be strong in the Italian-speaking Ticino region (50 per cent).
But the ballot is unlikely to be decided by voters with clear party affiliations, according to Longchamps.
"A lot will depend on those who haven't yet made up their minds," he said.
With five weeks still to go, Longchamps expects the political parties and organisations to step up their campaigns in a bid to sway those vital floating voters.
The survey is based on interviews with 1,212 people conducted August 8-12.
It is the second of three GfS polls ahead of the September 25 vote on granting citizens of the ten new EU member states access to the Swiss labour market.
Supporters cite opportunities for working abroad while opponents express fears of salary dumping.
49% yes, 36% no, 15% undecided
43% yes, 40% no, 17% undecided
Expected voter turnout: 49%
Margin of error: +/-3%