THERE are about 20km (12 miles)—and lots of checkpoints—between the official residence in Jerusalem of Binyamin Netanyahu, the Israeli prime minister, and the headquarters in Ramallah of Mahmoud Abbas, the Palestinian president. This week, as both leaders made simultaneous official visits to China, care was taken to keep a much greater distance between them. Their itineraries put them in different cities at all times.

Ever since the 1970s, when Henry Kissinger used shuttle diplomacy to marginalise the Soviet Union in much of the Arab world, America has dominated the geopolitics of the Middle East. Inevitably, this week’s visits prompted the idea that a rising China might be dabbling in the superpower sport of broking peace between the Jews and the Arabs.

Chinese experts spoke enthusiastically of this possibility in the national media. Hua Chunying, a spokeswoman for China’s foreign ministry, did her share to foster speculation about a potentially dramatic development, saying before the visits that “If the leaders of Palestine and Israel have the will to meet in China, China is willing to offer necessary assistance.”

In the end there was no handshake, nor was one ever likely. China’s rising political and economic might, and its growing appetite for energy, mean it has more at stake in the Middle East than it used to, but it still lacks the clout to knock heads together. Chinese aid to the Palestinian side is dwarfed by what America and others give. And despite growing bilateral trade and technology ties, China “is in no position to coerce Israel to do anything it doesn’t want,” says Robert Ross of Boston College.

Nor is it clear that China really has any desire to involve itself more deeply. It may seem as if China wants to play a bigger role, says Yin Gang of China’s Academy of Social Sciences, but the truth is that it is outsiders who really want this. “We have enough problems in our own neighbourhood.” Mr Yin predicts that China’s newly installed government will barely change the country’s long-standing policy of calling for peace, criticising the use of force and urging dialogue.

Meeting Mr Abbas in Beijing on May 6th, China’s new president, Xi Jinping, did just that. State media gave heavy coverage to the “four-point proposal” put forward by Mr Xi, but in its details the statement offered little that had not been said before, either by China or by other more established peace-brokers. His statement called for a settlement based on 1967 borders, a negotiating framework of “land for peace”, and an end to settlement-building and violence against civilians.

Such input from China, even if mainly symbolic, is probably more pleasing to Mr Abbas than to Mr Netanyahu. In the past China has been a strong supporter of the Palestinian cause. That stance has mellowed as China has become more pragmatic and less devoted to the brotherly solidarity it once showed for struggles in the poor world against colonialism and imperialism. In 1992 it established diplomatic relations with Israel.

There was one nasty diplomatic row in 2000 when America forced Israel to cancel the sale of an advanced radar system to China. Otherwise, ties have mostly been friendly and the value of bilateral trade has grown to nearly $10 billion. But, says Chen Yiyi, a scholar, Israel has yet to earn China’s sympathy. The number of pro-Palestinian articles in Chinese newspapers has increased dramatically in the past two decades. China is already pro-Palestine, wrote Mr Chen in Global Times, a state-run newspaper. “We can safely assume that the Chinese stance…in future will be as pro-Palestinian as today, if not more so.”

Foreign diplomats say Mr Netanyahu was never likely to show more than polite interest in Chinese involvement in the Palestinian issue. The public focus of his visit was on trade deals. The private focus was expected to be on China’s help in restraining Iran’s nuclear ambitions.

The worsening crisis in Syria also overshadowed Mr Netanyahu’s visit. China was quick to urge restraint after Israeli air strikes but scholars say Syria is not a big Chinese concern and, because China can buy its oil elsewhere, could present an opportunity for China to advance other policy goals it sees as more important.

The Chinese priority in Syria, as in so much else, is how to work with the United States. Some Chinese academics see hopeful signs that John Kerry, America’s new secretary of state, is less committed to the American “pivot” towards Asia than was his predecessor, Hillary Clinton. When China and Russia vetoed a UN Security Council peace plan for Syria in February 2012, Mrs Clinton called the move “despicable”. Says Mr Ross: “It may be time for China to figure out how they can start helping the United States in Syria.”