But when Estonia and Finland had the brain wave, they found the way blocked by the bureaucracy of the Australian Capital Territory.

In the end, the law had to be changed to allow the diplomatic co-existence in the elegant, modern Finnish-designed building on Darwin Avenue in Yarralumla.

Back in northern Europe, the two countries are neighbours, albeit ones separated by 87 kilometres of Baltic sea. They speak similar languages. Their peoples have similar sets of attitudes, no doubt formed by nights of four or five hours in summer and days of only four or five hours in winter.

And by proximity to the big bear of Russia. During the Cold War, Finland lived uneasily with its Soviet neighbour as a capitalist country on condition it kept quiet. Estonia was actually part of the USSR.

With the collapse of the Soviet Union in 1989, Estonia gained independence but it was only three years ago that the embassy in Canberra was established - in the Finnish embassy.

The ambassadors say it works well. They get on personally and there are no obvious disputes between their countries. They benefit from each other. The ferries that cross between the capitals back home make Helsinki the world's busiest passenger port.

But living in the same building is made easier because it's long and narrow like a ship - that was the concept the architect had for the glass, steel and concrete masterpiece.

Just like in smaller house shares, amity is easier if people can get away from each other. They have their own facilities at each end, so there are no housemates' arguments over who cleans the fridge. There is enough distance to make private phone calls.

The Finnish ambassador, Lars Backström, has his office at the prow and the Estonian ambassador, Andres Unga, at the stern. In between are the offices of their embassies divided by a deck where Finns and Estonians can meet and share coffee and, no doubt, gossip. Being a corner of Nordic Europe in Australia, there is a sauna at the back, which is open to both.

Both ambassadors were surprised when the original application to co-site was turned down by the Canberra authorities, particularly since, at the time, Canada and Australia wanted to share premises for their embassies in Kiev.

"We were rejected," Andres Unga of Estonia said. "It was a big surprise and disappointment."

The reason, apparently, was bureaucratic rather than on principle. There was a law going back to the foundation of Canberra as the national capital that simply forbade shared embassies. When the Estonian/Finnish request came in, there had to be a lot of lobbying and politicking but the law was finally changed.

During the process, the Estonians were in the building but, as the ambassador says, "we couldn't use our name and flag".

Now, they're together - albeit at each end of the ship.

"We had space available and we are very pleased that Estonia joined us," Finnish ambassador Backström said.

They share things like transport, taking rides together to functions. The Estonians borrow the Finnish mini-van.

"We have our own offices," Estonian ambassador Unga said. "We sit at our own tables.

"But often we sit down together and look at what is happening in Australian politics."

Which can be interesting. "I went on holiday and when I came back prime minister Turnbull had gone," Unga said.

The two men know each other. Both were their country's ambassadors in Beijing. They seem to have respect for each other and are easy in each other's company, particularly over coffee and cake in the Finnish ambassador's residence on the same site.

But countries never have completely identical interests, not even the closest of allies. In the case of Estonia and Finland, though, their interests coincide more than virtually any other. Both are wary of Russia; neither has territorial ambitions; both see trade as paramount.

Both have substantial communities in Australia. There are about 35,000 Finns and between 10,000 and 12,000 Estonians in Australia.

Estonia, in particular, has seen flights of migrants from Nazism and Communism, the refugees forming what became the expat community of Australians.

What do the Finns and Estonians back home think of Australia?

"They know about kangaroos and deadly snakes and spiders," ambassador Backström said.

What do they get wrong?

"What they get wrong is that they think it's warm all the year round," he said.

"And the cold," added his Estonian counterpart. "They can't imagine that it can go down to below minus."