As concern about North Korea’s bellicose behavior deepens, calls are growing among pundits and politicians in the United States for China to “do something” about its obnoxious ally. The underlying assumption is that Beijing has the power at least to compel Pyongyang to end its saber rattling and probably to force Kim Jong-un’s regime to mothball its nuclear and ballistic-missile programs.

As I’ve written elsewhere, there is a tendency in the West to overestimate China’s influence on North Korea — unless Beijing is willing to embrace the drastic option of severing food and energy shipments to the hermit republic. But the United States has given Chinese leaders no incentive to incur the risk of having the North Korean state unravel, which could lead to both a refugee crisis and the prospect of a united Korea allied militarily with the United States.

For Beijing to take such a gamble, either there would have to be a large potential reward for action or an equally large potential downside for inaction. Current U.S. policy includes neither feature, and that has to change. If Washington is not willing to offer Beijing the one “carrot” that might cause Chinese leaders to dump the country’s troublesome client — ending the U.S. alliance with Seoul upon Korean reunification — the Obama administration must boost China’s anxiety level.

The most effective way to do that is to invoke the specter that South Korea and Japan might decide to build their own nuclear arsenals if North Korea continues its menacing ways, especially its quest for nuclear weapons. Chinese officials would not be happy about a South Korean nuclear arsenal, and the last thing in the world they want to see is a nuclear-armed Japan.

Beijing has certainly noticed that sentiment is building in both neighbors for ending the commitment to remain nonnuclear. Two opinion polls taken in South Korea, including one by Gallup Korea, after the North’s February nuclear test found that more than 64 percent of respondents favored Seoul developing its own nuclear deterrent. During a visit to Washington, a prominent member of South Korea’s parliament, Chung Mong-Joon, bluntly stated that the time had come for South Korea to withdraw from the Nuclear Nonproliferation Treaty. Although public opinion in Japan has not yet produced a similar pronuclear majority, that once taboo view is now a significant factor among members of the country’s political elite — and China is worried.

But instead of heightening China’s anxiety about Japan and South Korea possibly acquiring nuclear capabilities, Washington has traditionally gone to great lengths to discourage its allies from even considering that course. During one of the periodic North Korean crises during the Bush administration, Secretary of State Condoleezza Rice assured both Tokyo and Seoul that the United States would defend those countries from North Korean aggression with “the full range” of U.S. weapons. Thus, Japan and South Korea would have no incentive to build nuclear deterrents of their own. During his just completed trip to East Asia, Secretary of State John Kerry likewise assured the allies that the United States would defend them by any means necessary.

Instead of putting such a public diplomatic leash on any nuclear ambitions by Japan and South Korea, U.S. officials should inform Beijing that if North Korea insists on crashing the global nuclear-weapons club, Washington will have no objections to Tokyo and Seoul following suit. Although the prospect of further nuclear proliferation in East Asia is not a pleasant one, not all forms of proliferation are equally bad, and we should stop acting as though they are.

The prospect of a nuclear-armed Japan and South Korea is one factor that might galvanize the Chinese to put intense pressure on Pyongyang to end its nuclear buildup and saber rattling. During an earlier North Korean crisis, Washington Post columnist Charles Krauthammer made that case bluntly. “If our nightmare is a nuclear North Korea, China’s is a nuclear Japan. It’s time to share the nightmares.”

His approach has considerable logic today as well. At a minimum, Washington should no longer go out of its way to alleviate Beijing’s uneasiness about that scenario.