The forced turn-back of asylum-seeker boats to Indonesia has overwhelming public support in Australia, bolstering Prime Minister Tony Abbott as he sits down on Wednesday with President Susilo Bambang Yudhoyono.
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A new poll also found almost two-thirds of Australians back spying operations in Indonesia, another flashpoint for Mr Abbott to navigate after last year's revelations that Australia bugged Mr Yudhoyono's telephone.
Yet in a surprise result, the public is just about as happy to treat America - or even New Zealand - as an intelligence target, a finding apparently at odds with Australia's strong support for the ANZUS alliance.
The annual Lowy Institute survey of attitudes on world affairs shows Australians are again warming to China, if not its leadership.
While Mr Abbott has said Japan is Australia's ''best friend'' in Asia, the public marginally favours China.
But the US remains a more popular country than China, with President Barack Obama most admired among a list of world leaders.
China's leader, Xi Jinping, ranks last. China is also thought to be a likely military threat some time in the next 20 years.
But it is on ties with Indonesia that people appear most concerned. Controversy over classified documents leaked by Edward Snowden and Indonesian anger about boats being turned back were the dominant themes of recent months.
Some 40 per cent believe relations with Indonesia are worsening, compared with 16 per cent in the survey last year.
While this is still below a low point of 47 per cent in 2006, shortly after the sentencing of Schapelle Corby, far fewer people see a prospect for improvement in the relationship.
President Yudhoyono finds little favour among Australians; 28 per cent reported no admiration for the Indonesian leader. This is despite Mr Abbott's assurance, repeated on Tuesday, ''he has been a great friend to Australia''.
Mr Abbott deflected questions about friction in the relationship over the boat turn-backs by pointing to the sharp drop in attempted voyages over recent months.
''Because none of them are making it to Australia, very few are leaving Indonesian shores. The whole point of leaving Indonesia is to get to Australia and if you never get to Australia, why bother leaving Indonesia?'' he said on ABC radio.
The Prime Minister's turn-back policy is backed by 71 per cent of Australians.
The Lowy poll ranks a list of ''threats to Australia's vital interests'', with international terrorism (65 per cent) and nuclear weapons in the hands of unfriendly countries (64 per cent) sparking most concern.
The nationwide survey of 1000 people, taken in February, also showed strong support for offshore processing of asylum seekers.
However, in a sign of community divisions over boat arrivals, 57 per cent of respondents disagreed that ''no asylum seeker coming to Australia by boat should be allowed to settle in Australia''.
