However, the scheme to eradicate mink on Lewis and Harris may take a few more years to ensure the islands are finally free of the animals.
The Hebridean Mink Project (HMP) has so far cost £6.4 million and caught more than 2200 animals.
The scientists behind it now believe there are just a handful left on the islands.
Now, in a bid to ensure the remainder do not meet up, breed and spoil the success of the last dozen years, scented trails are being laid in the hope they will go round in circles until they die out naturally over the next few years.
The non-native mink were introduced to the islands in the 1950s and 1960s in attempts at commercial mink farming in Lewis.
When that failed, the animals were released or escaped and spread rapidly, colonising areas of Lewis and Harris. Feral mink were first recorded in Lewis in 1969 and spread southwards, reaching South Uist by 2001.
That was the year the Hebridean Mink Project (HMP) was set up with the aim of protecting internationally important populations of wader birds.
Since then 2200 mink have been trapped and removed from Lewis, Harris and the Uists. Already some tern colonies are showing signs of recovery.
Iain Macleod, the Scottish Natural Heritage (SNH) scientist who manages the project, said it was impossible to tell yet whether the mink had been completely eradicated from Lewis and Harris.
He said: "It is very difficult to prove a negative. I personally think we have a small handful of animals left. But it could be 20 plus or minus 20.
"If there are only a few it's not absolutely vital we catch them all as long they don't meet up and mate.
"They only live for three or four years so we hope they will just die out. One of our methods is to create monitoring tunnels right across the islands, where we can see the footprints on clay paths."
He said they used a lure from America for the scented trails to attract the creatures into the tunnels.
The minks try to seek out their own kind by following it and this, in itself, disrupts their territorial behaviour.
He said: "So rather than going out looking for a mate and finding one, they think there is some locally and keep going round in circles."
It was hoped this last handful would be pushed to extinction in this way.
But computer-based modelling had produced different predictions of when the islands would be mink-free. These ranged from this year to 2021.
There is a general belief that North Uist, Benbecula and South Uist have been successfully cleared.
Traps with fish were laid there to catch hedgehogs for relocation which would attract mink if they were there. Mr Macleod said: "We are hopeful the job is done there, but we still need people to tell us of any possible sightings of mink and we will follow them up."
Meanwhile, Mr Macleod hit back at claims that, in Lewis, as the mink had gone the rat population was out of control to the point they were attacking cars.
He said: "There is no direct link. With these small rodents you need to kill 70% to 80% year on year to put them into decline.
"The important factors are the climate and food available, not the predators that eat them. If you looked at the savannah of Africa and saw a herd of 10,000 wildebeest walking across, and in the foreground there was a pride of lions, you would instinctively recognise the lions can't control these numbers. It's grass and water that do that."
However he said that, with the mink going, more people were keeping hens and chickens and feeding them, thus attracting rats.
Mr Macleod said the project had what was believed to be the largest trapping dataset in Britain.
He said: "This computer modelling exercise was carried out to help us understand how the mink population on Harris and Lewis has responded to the intensive and long-term trapping work.
"All the computer modelling does is add exhaustive support to the impression held by the project's staff, namely that the population of mink in Lewis and Harris is now extremely small."