When it comes to international summits, management of expectations is often the name of the game. No political leader wants to over-promise and then have to return home with their tail between their legs when they don't secure what they wanted.
And in the world of international summitry, no show is bigger than the United Nations Climate Change summit in Copenhagen, scheduled to begin on 7 December.
In recent weeks, world leaders have been busy downplaying public expectations about Copenhagen's chances of producing a successor to the Kyoto protocol. But the mood has changed in recent days and for a specific reason: politicians began to talk numbers.
First there came an offer from the Obama administration to cut America's emissions by 17 per cent by 2020. There followed an announcement from Beijing that China will decrease its economy's carbon intensity by 45 per cent by the end of the next decade.
Neither commitment is adequate. The US offer is to cut emissions relative to 2005 levels and is much less significant than the EU pledge to cut emissions by 20 per cent on 1990 levels by 2020. And under Beijing's plans, China's carbon emissions would continue to rise overall.
These pledges give the world no chance of escaping a C rise in global temperatures, the threshold of dangerous planetary heating. To do that, our global emissions would need to peak and start to decline within 15 to 20 years. Nothing announced this week would set us on that road.
Yet it would be wrong not to acknowledge that these two announcements represent a step in the right direction. The US will now go into negotiations in the Danish capital with a clear offer to cut emissions if other nations sign up to a binding deal. And China is no longer insisting that the burden of cutting emissions must fall exclusively on the developed world. That is a big shift from both nations.
Such movement from "the big two", which together account for some 40 per cent of the world's emissions, makes a serious deal at Copenhagen much more likely. Numbers are now on the table, rather than simply good intentions.
China's move is likely to help bring India, another rising giant and the world's fourth largest emitter of greenhouse gases, on board. Delhi's environment minister, Jairam Ramesh, admitted this week that "China has given us a wake-up call". That is certainly good news; the world needs those alarm bells to be ringing.
Further good news came this week with the announcement that President Obama will attend the summit in person. The presence of the leader of the world's most powerful nation, albeit at the beginning of the summit rather than the conclusion, should be a galvanising influence.
Delegates should be aiming to produce a binding deal complete with legally binding emission cuts in Copenhagen. But if such a deal cannot be done next month, the world needs an unambiguous agreement that a successor treaty to Kyoto will be signed in 2010; anything less would be a disastrous failure.
After a depressing few weeks, cautious optimism has returned to the Copenhagen process. Expectations have been buoyed. It is now incumbent on global leaders to deliver in the Danish capital.