Kim Jong-un’s quest for nuclear weapons and inter-continental missiles is rational. The ability to strike American allies, South Korea and Japan, and even the United States itself with nuclear weapons is the most obvious deterrent against any effort to end his regime. If the threat posed by North Korea’s nuclear weapons were easy to solve, the problem would have been solved long ago. In addressing the threat from North Korea, a very real threat in which the North Korean’s could develop ICBMs that could deliver nuclear weapons to the American mainland, the United States must confront two very difficult challenges.

First, the U.S. cannot act unilaterally, especially if it acts alone, without risking a devastating country strike against South Korea. Hundreds of thousands of people or more could be killed in Seoul, which is within the range of conventional weapons from North Korea. If South Korea suffered such a large loss of life as a result of a basically unilateral American strike, it would be the end not only of the South Korean-U.S. alliance but of NATO as well. No country will tie itself to the United States if the United States through its own actions can take measures that would result in hundreds of thousands of citizens in other countries being killed.

Second, China is the only country that might—and the key word here is “might”—be able to engineer a leadership change in North Korea and an end to the North Korean nuclear and missile program. If China were confident that it could alter the leadership in North Korea and introduce Chinese-like policies for economic development, it probably would have done so long ago. A greater role for China, which the Trump administration has embraced, is not a guarantee of success but it is the only possible path to success.

Since the United States cannot act unilaterally and since China is the only country that just might be able to change North Korean policies, the basic question is this: What would convince the Chinese to adopt a more risk-acceptant stance, to pressure the North to abandon its nuclear ambitions, recognizing that the outcome of any such effort would be uncertain?

The United States, South Korea, and China do not have the same preference orderings. The first best option for all of the most relevant parties is a soft landing for North Korea in which the regime endures but minus Kim, the North gives up its nuclear weapons and missiles, and economic reforms are introduced that mirror those that that Deng Xiaoping brought to China. The next best option for the United States, however, is the denuclearization of North Korea and the end of its missile program even if this means a messy implosion of the regime. For South Korea and China, the implosion of the North Korean regime would present huge and probably unmanageable challenges. The population of North Korea is about 25 million, half that of South Korea, and its per capita income in nominal terms is less than three percent that of the South. The North Korean people have lived under a repressive dictatorship with limited access to outside information for several generations. If the North Korean regime collapsed, would China and South Korea shoot people at the Yalu River or the DMZ? For both countries, such a prospect would be a nightmare.

The most obvious option, direct American negotiations with North Korea, is a non-starter. The North has demanded for years that the United States sign a peace treaty that would recognize the regime and guarantee its security. Successive American administrations have resisted and not just because there would be a political cost for a picture of any American president shaking hands with a Kim. Regardless of the political fallout in the United States, it is hard to see how the United States could make a credible commitment to the North—that is, a commitment that the North would believe—and it is difficult to see how North Korea could make a credible commitment to the U.S. to give up its nuclear and missile program. Why would they believe us? Why would we believe them? Regardless of the sequencing of any agreement, whether recognition came before de-nuclearization or vice versa, credibility problems would remain. It is hard to imagine that the North would, in the end, give up its nuclear arsenal. The credibility issues cannot be resolved. So direct negotiations are a dead end.

A more appealing, at least possible, option is the replacement of Kim Jung-un with a leader in the North who might support different policies. The only country that could achieve such an outcome would be China. If, however, leadership change in the North were easy, China would have done it long ago. Pressuring the North would be risky for China. What might make the Chinese more likely to act? One possibility is that the U.S. threatens to take out the North Korean program on its own. To the extent that there is any strategic thinking in the present administration, the timing of the American missile strike against Syria might be an attempt to send such a signal, but a unilateral attack by the United States could result in a devastating counter-blow against Seoul, would put all American alliances at risk, and would be a gift to China. A unilateral attack is not a credible threat.

If an American threat to unilaterally act against the North is not credible, what else might prompt China into a more risk-acceptant policy with regard to North Korea? What China above all does not want is a strengthening of the American position in East Asia and the western Pacific. A unified Korea allied with the United States would be unacceptable to China, a clear signal that Chinese power had peaked. A Korean peninsula still divided, with a North Korea bound closely to China and Kim Jong-un gone, and a South Korea free of American troops would be an attractive option for China.

Withdrawing all American troops from South Korea even if an alliance between South Korea and the United States remains, would be a costly move for the United States, not just cheap talk. The cost, however, has been reduced by the Trump administration, which has irretrievably brought into question the commitment of the United States to its allies. Regardless of what Trump does from here on out, America’s allies will be searching for alternatives; this includes not just those in Asia but those in Europe as well. The question that the French asked in the 1950s in deciding to develop their own nuclear capacity was whether the United States would give up New York for Paris? It never had an unambiguous answer. The robustness of the American alliance system, especially after the collapse of the Soviet Union, depended on two foundations: formal alliance commitments and presidential rhetoric. Trump has already destroyed one of those foundations.

So there is a deal that the United States could credibly offer to China: leadership change in North Korea and the end to nuclear and missile programs there, in exchange for the withdrawal of American troops from the peninsula. All U.S. forces would be removed, if China actually succeeded in engineering the ouster of Kim Jung-un and an associated end to its nuclear and missile programs. A North Korean commitment to end its nuclear program made by a leader dependent on China would be more credible than any commitment made by Kim.

This strikes me as the most plausible deal in terms of yielding a way forward. Direct negotiations between the United States and North Korea will not work, because the United States cannot credibly commit to not attacking the North and because a North Korean regime led by Kim Jung-un cannot credibly promise to end its nuclear and missile programs. Offering up American troops stationed in South Korea is a more promising option. If it were successful, China would get a subservient ally and a demonstration of its ability to change American behavior in East Asia. South Korea would get a reduced threat from the North, but at the cost of removing the American tripwire. The United States would get an end to the threat of a North Korean nuclear attack, but at the cost of altering its alliance. Of course, the Chinese might fail.

In that case, the only option for the United States would be the one that we have implicitly relied on, which is deterrence: Attack us and you will be dead, literally dead.