Why the summit? Businesswise, ASEAN matters to America. Taken together, which increasingly it wants to be, its members would be the world’s seventh-biggest economy. American foreign investment in ASEAN was $226 billion in 2014, more than in China, South Korea and Japan combined. South-East Asia is young and economically vibrant.

Second, democracy in South-East Asia needs the kind of boost Mr Obama’s attentions will provide. Myanmar’s extraordinary democratic transition remains fragile. In Thailand politics has lurched backwards since Prayuth Chan-ocha’s coup of May 2014 suspended democracy. This irks America, Thailand’s chief ally. As the annual Cobra Gold military exercises, involving Thailand, America and 25 other countries, began this week, the American ambassador in Bangkok called for a return to elected government. Meanwhile, in Malaysia the money scandals and racial politics of the prime minister, Najib Razak, are undermining democratic institutions. A little lecturing by Mr Obama behind closed doors would not hurt.

But, above all, American officials boast that the gathering underlines the success of Mr Obama’s “pivot” or “rebalancing” towards Asia. That is disingenuous, given the scant material evidence of a pivot. Certainly, Mr Obama has attended to South-East Asia more than his predecessors did. No president has made more trips to the region, with unprecedented visits to Cambodia and Myanmar and, later this year, to Laos and perhaps Vietnam, once America’s nemesis. Mr Obama has also appointed America’s first ambassador to ASEAN and has regularly attended ASEAN leaders’ meetings. And having spent four happy childhood years in Jakarta, Indonesia’s capital, he has a personal link with the region that is shared by no previous president.

Yet leaders are coming to Sunnylands less because of Mr Obama’s engagement than because of China and its recent assertiveness. China’s once-vaunted “smile diplomacy” in the region has seemed to turn to scowl. Its expansive claims in the South China Sea have greatly strained relations with neighbours with overlapping claims. In 2014 China dragged an oil rig into Vietnam’s territorial waters, provoking confrontations at sea and violent anti-Chinese protests on land. Chinese aggression towards the Philippines in disputed waters near the Spratly Islands emboldened the government of Benigno Aquino to ask an international tribunal in The Hague to adjudicate on the nature of China’s South China Sea claims, which are as legally vague as they are grabby. Meanwhile, ASEAN members have boosted naval co-operation and defence ties with America, Australia, Japan and India. There is even talk of tensions driving a naval arms race.

Some now divine a softening on China’s part. Perhaps it sees the public-relations damage. Perhaps it remembers how, in 2010-11, Myanmar plopped out of China’s orbit and into the West’s. At any rate, some of the smiles are being turned back on. Under its “one belt, one road” initiative of building globe-girdling trade links, China is promising to invest in ports and railways across South-East Asia, assisted by another Chinese-led venture, the new Asian Infrastructure Investment Bank. (Besides the diplomatic payoff, this is intended to provide an outlet for goods from half-idle Chinese factories.) China has always welcomed South-East Asian autocrats such as Mr Prayuth and Hun Sen of Cambodia. Now even democrats with Nobel peace prizes are going to Beijing. Last year President Xi Jinping received Myanmar’s Aung San Suu Kyi, who had long been shunned.

American policymakers sneer that, with its chequebook diplomacy, China is crudely attempting to buy influence across the region. Perhaps that is true. But if so, it hints that China understands the damage its sabre-rattling has done and is trying to make amends. ASEAN members no doubt appreciate its largesse. However, they remain suspicious of its intentions. So they turn to America as a counterweight to Chinese influence. Much like a Yorkshire Terrier sharing its bed with a Great Dane, small countries bordering big ones tend to be nervous: even if the big dog is inclined to be good-natured, it could still roll over and crush the Yorkie. Just ask Canada or Mexico.

Hedges make good neighbours

So the Sunnylands summit cannot have pleased China—especially since it was there that Mr Obama welcomed Mr Xi for a groundbreaking love-in in 2013. South-East Asian diplomats crow that the choice of place shows that America considers ASEAN to be just as important as China. Yet the meeting between the two presidents was an introduction. This one will be more like a valediction. At least five of the 11 leaders gathering in California, including Mr Obama, are on their way out of office. And among those who will remain, Mr Prayuth and Mr Hun Sen preside over dangerously fragile polities.

The summit is unlikely to yield much more than the promise of future summits. But for ASEAN, obsessed with process more than with destinations, that may be just fine, with America remaining a hedge against China. If China really wants the region more firmly in its orbit, it will have to do a better job of speaking softly and concealing the stick.