If you followed the conventional narrative of the last few months, you would readily believe that America’s relations with China have fallen to a new low, disappointing a naïve and optimistic Obama administration and revealing a belligerent and arrogant China. But in the past three days, the Chinese have announced that President Hu Jintao will attend the Nuclear Security Summit in Washington later this month, and signaled that they may support new sanctions against Iran.

The truth is that official Washington and official Beijing have not gone through radical or even noticeable adjustments in their major policies toward each other. Rather, as relations went through a cycle of familiar ebbs and flows, China’s propaganda machine slid out of sync with its national interests.

Case in point: on January 27, President Obama approved a $6.4 billion package of arms sales for Taiwan. Chinese spokesmen responded with stronger rhetoric than they had issued after previous rounds of arms sales, and made new threats to sanction the American companies involved. Yet the U.S. decision avoided weapons judged exceptionally sensitive to China and largely complemented a list that George W. Bush had approved in 2008, which did not receive comparable responses. Moreover, China’s reaction is in reality no different from what it did after previous arms sales, and maybe even a little more cautious in halting only a “portion” of military-to-military exchanges, rather than all of them, as in 2008.

In February, when Obama received the Dalai Lama at the White House, Beijing’s warnings were dire and omnipresent. But after the president received His Holiness in the semi-official manner of all his earlier visits—except the presentation of the Congressional Gold Medal in 2007—Beijing’s warnings looked overwrought. The official response was actually worded more mildly than in 2007, reflecting the restored realities of the Dalai Lama’s reception.

Then, within days of the dreaded meeting, China invited senior administration officials responsible for China, Deputy Secretary of State James Steinberg and National Security Council Senior Director Jeffrey Bader, to visit Beijing. From Chinese officials’ interactions with a host of contacts, including this author, it became clear that they had recognized that they had let their rhetoric get ahead of their interests, and were looking for a way to climb down.

Chinese officials planted hints that the United States should break the diplomatic logjam and save China’s face, perhaps by repeating portions of the joint statement issued by Chinese President Hu Jintao and Obama during his state visit to Beijing in November. At this point, the Obama administration officials showed a steadier hand and calmer demeanor than the American or Chinese media or the U.S. Congress.

U.S. officials found opportunities to repeat publicly tested and uncontroversial principles of American relations with China: the One China policy, respect for China’s territorial integrity, and the like. Last week, Mr. Steinberg called a quick press conference to repeat China policy bromides. The Americans then left the Chinese to fashion these into the ladder they needed to climb down from the high rhetoric of the preceding months.

Chinese officials, pressed for time in deciding whether or not their leader should attend April’s rapidly approaching Nuclear Security Summit in Washington, abandoned their recent heated rhetoric, seeking only assurances that he would not “lose face.” The Chinese considered the merits of attending and hosting such a meeting and drew their own appropriate conclusion: that Hu Jintao should naturally attend the meeting, as his absence would be problematic and could send an unintended signal.

Finally, Beijing assigned a new ambassador to Washington, and when he presented his credentials, the Obama administration skillfully capitalized on the occasion to repeat the fundamentals of U.S. policy and urge Chinese cooperation. The Beijing journal China Daily referred to these gestures in an article relating that the U.S. had “sounded placatory notes.” The article quoted President Obama expressing his desire “to ‘further develop’ a positive relationship with China.” By repeating the story, Beijing is telling its people that Washington has turned around, and it is back to business as usual with the Americans. The rhetoric has cooled, but it is Beijing that has turned.

Good enough for government work. So, what next? There are several potentially sensitive items on the U.S.-China agenda in the coming months, including the impending Nuclear Posture Review, a Department of Defense Report on Chinese military power, and of course the Treasury Department report to Congress on China’s currency misalignment—the latter getting the most attention in China and the United States.

To meet U.S. concerns, which President Obama raised in his meeting with China’s new ambassador, China must show cooperation on “rebalancing” the global economy—code words for currency reform—and sanctioning Iran.

On the question of whether and by how much China undervalues the renminbi, the improving trade figures of the past six months (the congressionally required time span and factual basis for the review) make a strong case against citing China formally for currency manipulation. Citing China immediately after the presumed departure of the Chinese president would certainly be seen as a clumsy diplomatic snub.

Moreover, in May, Treasury Secretary Timothy Geithner and Secretary of State Clinton will lead a large delegation to discuss how to deal with exactly this problem, i.e., how to “rebalance” the two economies after the recession. Thus, there is no hurry to cite China in April. China recently signaled at the UN that it is prepared to do more on Iran.

In the longer term, however, Chinese officials must reflect on how they allowed the recent flare-up in their diplomatic posture to run against their interests. China seems intoxicated by its language of “core interests” in Taiwan and Tibet, and has forgotten its “broader interests” in trade, development and a “peaceful environment.”

The people of China have a sense that the economic crisis has proved China’s methods superior, a sense that has bred an undue hot-headedness. With Presidents Obama and Hu preparing to mend fences, Chinese officials should begin asking themselves what they can do to help repair the damage.