It seemed the invitation of a lifetime, to live on a beautiful Hebridean island barely a mile wide, with no street lights, no pubs and no noisy roads. The opportunity to move to Canna attracted more than 350 applications from around the world.

But for several of the families who traded urban life for one of the smallest inhabited islands in Britain – after a global competition to find people to live there – the dream has paled.

Three couples, including the island's teacher and a retired couple who took over the guesthouse, have decided to leave, cutting Canna's population down to just 11.

They have criticised the restrictive rules governing life on Canna, which is owned and protected by the National Trust for Scotland. But social and private tensions too are said to have influenced one or two families to relocate, forcing the trust to search for new residents.

It announced on Wednesday that a couple from Inverness-shire would soon move on to the island, to take over a refurbished cottage. Alison and Duncan Spence, who have two young children, have previously lived on an island off Papua New Guinea, and would take on a variety of island jobs. They said they were ready for the challenge.

"We were looking for a change and felt that, after being in Laggan for ten years, it was time for something new," Alison Spence said. "We thought it might be just what we were looking for. It's very different and a new way of life, but we're prepared and positive about that."

The trust, which was given the island by the celebrated Gaelic folklorist John Lorne Campbell in 1981, said it was delighted. However the crisis has pushed the trust into re-examining its policies, and again exposed the stresses of living in a small community struggling to cope with decades of depopulation and enduring Canna's often harsh, long winters.

Alexander Bennett, the trust's Highlands and islands manager, said the trust and islanders knew stronger community bonds were needed. "We're disappointed, can't deny that, but we're being realistic. People have to react to circumstances and if people have to move on, we have to accept that," he said.

"But we see it as a chance to bring in fresh blood and hopefully find a balance. It will work for some, but it won't work for others. People come in with expectations and if things conspire not to meet those expectations, people become disillusioned."

Geoff and Eilidh Soe-Paing are to leave later this year after becoming frustrated that the trust's ownership rules meant they could not build and then own their own home. Eilidh runs the island's small primary school.

Speaking to the BBC in May, Geoff Soe-Paing said: "There should be attempts made to let them have a little bit of hand in their own destiny and give them not just lip service to community empowerment.

"People will come and go and that is the short-term viewpoint of the trust. Why can't we keep people here? Surely that is the question."

Their criticisms are shared by Sheila Gunn and John Clare, who moved to Canna from the coastal town of Oban in 2007 after the trust issued their global appeal. After running the island's bed and breakfast – Canna hosts roughly 30,000 visitors a year, often on yachts cruising the Hebrides – they felt unable to put down firm roots and are moving to Eigg, the island close by where life has been revolutionised by a community buy-out.

Neil and Deborah Baker, with their children Elinor and Anwen – the second family selected from the 350 applicants in 2007 – have moved to Islay in the southern Hebrides. Neil Baker was on a fixed term contract to restore the treasured garden created by Lorne Campbell and his wife Margaret Fay Shaw at Canna House, but has left early after finding another job.

Bennett said the trust was unable under the terms of its ownership of Canna to allow people to own their homes outright, while Scottish tenancy law limited leases to just 20 years. But the trust was now considering whether it could have shared ownership agreements or introduce rolling leases.

"We're trying to empower the community to organise themselves on a daily basis through the Canna community association but some people might have aspirations to go beyond that," he said. "We're trying to work in partnership with that.

"We want to look at this positively, because the future success of Canna is having families there who can contribute to that sustainability. [But] the rest is up to them. We can't dictate the way people live their lives; all we can do is put the infrastructure in place.

"It has made Canna think very clearly about their future and it has made the core Canna community stronger."