The right-wing Swiss People's Party is the country's most popular, according to the first poll on voting intentions ahead of next year's parliamentary elections.
The survey showed that the People's Party would gain 25 per cent of votes cast, making it the largest party outright for the first time.
At the last election in 1999, the party won 22.5 per cent of the vote, the same as the centre-left Social Democratic Party.
However, there is little support for giving the People's Party another cabinet seat - it currently has one, while the other three parties in government each hold two.
Exactly half of those polled were against the idea of giving a second seat to the People's Party.
The big loser in next year's elections could be the Christian Democratic Party, already the smallest of the four in government.
Just 14 per cent of those questioned said they would vote for the centre-right party - compared with 15.9 per cent at the last election.
The vote for the other centre-right party, the Radical Party, would hold steady at 19.9 per cent, while the Social Democrats would increase their share to 23.3 per cent of the vote.
Setting the agenda
The survey, carried out on behalf of the Swiss Broadcasting Corporation, shows that both the People's Party and the Social Democrats are most competent in addressing issues of concern to voters.
The Social Democrats are seen as the strongest party in the areas of unemployment, state pensions and health, although in each case the combined rating of the three other parties is higher.
On the issue of asylum, the People's Party is the clear leader with 35 per cent of those questioned believing it has the greatest expertise, compared to just 11 per cent for the Social Democrats.
The parties on the right also dominate on the issues of tax and finance, with the People's Party once again coming out on top.
Reasons for change
Another factor seen as influencing the change in voting intentions is the increase in the number of people planning to vote - up from 43 per cent in 1999 to 49 per cent.
First-time voters also make their impact, accounting for 14 per cent of those who intend to vote, with the Social Democrats benefiting most (32 per cent), followed by the People's Party (23 per cent).
The rightwing has proved the most adept in wooing floating voters from the parties in government, while new supporters of the Social Democrats are drawn from marginal parties, such as the Greens.
No change to the Magic Formula
The People's Party's gains in the popular vote and the improved image of its leaders would not automatically guarantee it a second cabinet post, under the so-called Magic Formula, which shares out portfolios among the four main parties.
Although 80 per cent of People's Party supporters would like to see a change to the "Magic Formula" that has existed since 1959, only 32 per cent of the electorate were in favour and exactly half of all voters rejected a change in the allocation of seats.
The "Magic Formula" allocates two cabinet seats to the Social Democrats, the Radicals and the Christian Democrats and just one to the People's Party.
Opposition was strongest among Social Democrat supporters at 81 per cent, with 65 per cent of Radical and Christian Democrat supporters also resistant to change.
The poll was carried out by the GfS research institute in Bern on behalf of the Swiss Broadcasting Corporation and three national newspapers.
It was conducted over a ten-day period at the beginning of October among 2004 people. The margin of error is plus or minus 1.8 per cent.
swissinfo, Jonathan Summerton
A recent poll shows the right-wing Swiss People's Party is the most popular.
The Christian Democrats could be the biggest loser in next year's elections.
With an increasing percentage of the popular vote, the People's Party hopes to gain a second seat in the cabinet.