A declaration by Secretary of State Rex W. Tillerson that the United States would consider pre-emptive military action against North Korea raises a question that has dogged American military planners for 20 years: How could this be made to work?

The United States has long threatened force. The sincerity of such threats has always been ambiguous, as they are often meant less to prepare for war than to act as a deterrent to North Korea and a reassurance of the commitment by the United States to South Korea.

But there is a reason that, even as North Korea’s weapons programs have passed red line after red line, the United States has never followed through.

Almost any plan would bring a high risk of unintended escalation to all-out war, analysts believe. It would place millions of South Korean and Japanese civilians in the cross hairs of North Korean weapons with few guaranteed benefits.

That officials would even raise a pre-emptive attack shows the growing severity of the crisis, but the problems associated with any such plan demonstrate why that crisis has remained unsolved for two decades.

Three Unappealing Choices

A pre-emptive attack can generally mean one of three things. Mr. Tillerson, in keeping with past American statements, did not clarify which of those options were on the table but ruled none of them out.

Here is a brief guide to each:

1. A Single Strike to Halt a Missile Launch

How it would work:
Mike Mullen, a former chairman of the Joint Chiefs of Staff, said in September at the Council on Foreign Relations that such an
attack would be more “self-defense” than pre-emption.

If North Korea appears poised to launch a nuclear-armed missile, he said, American strikes could “take out launch capabilities on the launchpad or take them out once they’re launched.”

The challenge:
It may not be so easy as hitting launchpads out in the open. In wartime, North Korea would probably use mobile launchers, hidden around the country in locations such as tunnels. Striking every launcher before it could be used would be difficult.

The risk:
This would almost certainly be too late to prevent all nuclear missiles from getting off the ground and, given that missile defense is no guarantee, through to their targets.

2. A Set of Strikes to Devastate the Arsenal

How it would work:
Striking nuclear and missile facilities would delay the programs and pressure Pyongyang to surrender them. Cyberattacks, launched alongside or instead of physical attacks, could sabotage the programs and disrupt the military command.

The challenge:
Because North Korea’s program is indigenous rather than imported from abroad, the country has the know-how to replace destroyed facilities, making setbacks temporary. It would be difficult to strike existing missiles hidden around the country, most likely leaving much of the threat in place.

The risk:
Even a limited attack would probably prompt retaliation. An attack broad enough to seriously degrade the program could provoke North Korean fears of an invasion or an assassination attempt, potentially leading to all-out war.

3. A War Launched on American Terms

How it would work: The United States would initiate a war to destroy the North Korean government outright, much as in Iraq in 2003.

The challenge:
North Korea’s war plans are thought to call for extensive nuclear strikes to halt any invasion.

The risk:
North Korea would almost certainly succeed in launching some nuclear and chemical weapons, potentially killing millions.

Any plan faces a common set of problems that are both essential to overcome and, so far, have proved insurmountable.

The Retaliation Problem

For all of the United States’ military superiority, North Korea has one significant advantage: its willingness to accept risk.

This allows the country to retaliate against any limited strikes by imposing costs that are disproportionately difficult for its adversaries to bear.

North Korea can retaliate, for instance, by launching cyberattacks, as it is suspected to have done in 2013 against South Korea’s banking system and in 2014 against Sony Pictures.

It can stir up the risk of conflict, as it did with provocations in 2013. This benefits North Korea’s leadership, rallying citizens around the state
narrative of a glorious struggle. American, South Korean and Japanese civilians are less willing to accept the looming threat of war.

Mark Fitzpatrick, a scholar at the International Institute for Strategic Studies, wrote on the think tank’s website that strike plans could face heavy opposition from South Korean and Japanese leaders, whose citizens “would bear the brunt of the retaliation.” That opposition could limit American military options.

The country has also shown willingness to use violence that falls just under the threshold for war, for example shelling a South Korean island and sinking a South Korean ship, both in 2010.

Many analysts believe that the recent assassination of Kim Jong-un’s half brother, by VX nerve agent in the Kuala Lumpur international airport, was intended, in part, as a demonstration of North Korea’s willingness to use chemical weapons abroad and in civilian areas.

Any limited American attack plan would have to assume such retaliation — a potentially high cost to pay for strikes that would probably impose only temporary delays on the country’s nuclear development.

The Escalation Problem

North Korea knows it would probably lose any war. Should one occur, its plans call for a full-scale, last-ditch retaliation to stop the Americans in their tracks.

This strategy, borne of desperation, creates a risk that has long chastened American war planners: that North Korea would perceive even a limited strike as the start of a war and respond with its full arsenal.

Jeffrey Lewis, a North Korea expert at the Middlebury Institute of International Studies, recalled a 1969 episode in which North Korea shot down a United States Navy plane, killing 31.

The Nixon administration, he said, never retaliated because it could find no options that were “tough enough to punish the North Koreans, but not so tough that the North Koreans will think it’s a general attack,” setting off an all-out war.

That has been the problem ever since, Mr. Lewis said: “News flash, these Venn diagrams do not overlap.”

As North Korea’s nuclear capability has grown, the distance between a single attack and all-out war has shortened. Paradoxically, the heightened fear of escalation also makes it likelier.

“If there were ever a conflict, Pyongyang would have nowhere else to go but up the escalation ladder after artillery except to its nuclear weapons,”
Victor Cha, who served as the Asian affairs director on George W. Bush’s National Security Council, wrote in a September column in a South Korean newspaper.

That threat goes both ways, Mr. Cha wrote, because it “compels the United States to pre-emptively attack the nuclear forces at the first sign of conflict.”

A full war, entered deliberately or accidentally, would risk terrible costs.

Gen. Curtis M. Scaparrotti told a congressional committee in 2016, when he was commander of United States forces in South Korea, that war with North Korea “would be more akin to the Korean War and World War II — very complex, probably high casualty.”

Analysts doubt that the United States could reproduce the rapid military victory it achieved against Iraq in 2003. In the event of war, North Korean plans are thought to call for nuclear attacks against major ports and air bases in South Korea and Japan, halting any American invasion before it could fully begin.

In the meantime, nuclear and chemical strikes against major population centers would be intended to shock the world into capitulating. Missile defense would be of limited use against short-range rockets and of no use against North Korea’s hundreds of artillery pieces, many of which target Seoul, the South Korean capital.

The Strategy Problem

Potentially the hardest question of all is whether such plans would achieve American strategic aims.

Military strikes may be an imperfect tool, analysts say, for solving what is essentially a political problem: the leadership’s belief that it requires an advanced nuclear program to survive.

Strikes short of war would risk deepening, rather than altering, this calculus. Strikes that led to war would risk exactly the nuclear exchange they are meant to forestall.

Yet the United States has long maintained attack plans, illustrating the growing urgency of the North Korean crisis as well as how difficult it has become to solve.

“It’s a bad strategic idea, but you can understand why military planners would gravitate toward it,” Mr. Lewis said, calling the plans “the best of a bad lot.”