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WASHINGTON -- South Korea's new president and President Bush agreed last week that they "will not tolerate nuclear weapons in North Korea." But tolerance is a relative thing, which is why they danced around what strategy is most likely to prevent North Korea from turning a suspected small nuclear arsenal into a big one.

The most intriguing of those strategies appears to be straight out of another era of White House confrontations with Communist leaders intent on building nuclear arsenals: President John F. Kennedy's response to the Cuban missile crisis.

If negotiations with North Korea fail, the list of options kept in a White House safe, officials say, calls for a selective but escalating series of "interdictions" of cargo from the starving North. First, freighters suspected of carrying missiles would be stopped; then cargo ships that might have cocaine, counterfeit dollars or, the biggest nightmare, bomb-grade plutonium.

At the Pentagon, officials talk of a more audacious quarantine: trying to convince the Chinese to cut off the country's oil. The idea, as developed in a classified memorandum that Defense Secretary Donald H. Rumsfeld circulated last month, is to keep squeezing the North Korean leaders until they collapse. "You let in food," one senior Korea expert in the administration said, describing the memo, "but nothing else."

All this seems anathema to South Korea's president, Roh Moo Hyun, who said repeatedly that North Korea needs some grand bargain: security guarantees and the prospect of economic integration in return for the end of its nuclear program.

Both he and Mr. Bush, he said, seek a "peaceful solution." But their ideas of what makes a peaceful solution -- what mix of threats and incentives -- may conflict.

Mr. Roh envisions months of flexibility, offering concessions to figure out the North's price for giving up its nukes. "The stronger party can afford to show some flexibility," he said on Monday, adding he was "very concerned" about the influence of the hawks in the Bush administration, who advocate aggressive measures.

The quarantine idea has become a favorite of those hawks, because it stops short of attacking North Korea's nuclear sites, and risking a counterattack on Seoul. Mr. Rumsfeld and Vice President Cheney, among others, suspect that North Korea will never come clean about all its nuclear projects, and that it will respect a show of force on the open seas. They assert that even if the North agreed to stop making weapons, Washington would never be certain it found every facility. "How will we ever know that they have revealed every secret project, and opened every cave?" one senior aide asked last week. "We won't."

So the strategy for the next few months is to pursue negotiations with North Korea -- with Chinese officials in the room, and perhaps the South Koreans and Japanese as well. But no matter how big the table, many here doubt that North Korea will agree to dismantle their nuclear weapons.

Then come the "interdictions," some of which have already begun on a small scale. Spain, acting on American intelligence, used a pretext to board a North Korean ship carrying missiles last year -- but after protests from Yemen, which had paid millions for the missiles, Mr. Bush let the shipment through. (The Spanish were furious, having put their special forces at risk.)

Then, a few weeks ago, Australia seized a North Korean ship loaded with drugs.

But turning those interdictions into a strategy may prove difficult. The United States Navy carried out the Cuban quarantine itself; this one would require nervous South Korean and Japanese politicians risking a confrontation with an angry neighbor, as well as the cooperation of the Chinese. China, concerned that refugees would flood across the border, fears a collapse of the North Korean government.

"It's a very different strategy than what we pursued in Iraq, reflecting the fact that it is a very different kind of problem," one of Mr. Bush's senior aides said the other day.

The United States does not have the authority to board any ship suspected of carrying missiles. "If you had a Security Council resolution, it could give you rights to board a ship on the high seas, and search it and confiscate proscribed items," said Robert J. Einhorn, who served as the head of nonproliferation in the State Department under President Clinton. "On the other hand, if we were sure that Taepo-Dong missiles were on a North Korean ship headed to Iran," he said, referring to North Korea's long-range missile, "I'm sure that, in the current environment, we would board it and seize the cargo."

Small bits of plutonium, however, are a more complex matter. They could be slipped out in a backpack, or on an ox. "If it is in a lead-lined box, it would be hard to pick up, unless you knew where to look," Mr. Einhorn said. The intelligence agencies have warned that tracking such shipments would be difficult.

In the end, it is the prospect that North Korea could sell its bomb-grade material that has Washington the most worried. It has sold just about every kind of weapon it ever produced. That is something no one thought the Cubans would do in 1962, and it is what makes this crisis, in many ways, just as tricky to handle.