THE UNITED States and its allies have responded to Russia’s invasion of Crimea with a flurry of diplomacy aimed at persuading Moscow to accept negotiation and an eventual compromise, with a gently escalating sequence of sanctions as the alternative. Vladi­mir Putin’s answering strategy has looked something like the opposite: the embrace of extreme options that may allow him to present the unacceptable as a reasonable outcome.

Last Saturday, Mr. Putin’s rubber-stamp Federation Council granted him permission to invade all of Ukraine. When Mr. Putin announced Tuesday that he saw no cause, for now, to move his troops beyond Crimea, markets and European governments breathed a sigh of relief. Senior U.S. officials said they were holding off on sanctions that might genuinely cause the Kremlin pain, such as asset freezes, and keeping them in reserve in the event of a Russian invasion of eastern Ukraine.

As a result, the ongoing invasion of Crimea by thousands of Russian troops has been lightly punished. A handful of Russians have been banned from receiving U.S. visas, and routine military and trade talks with Moscow have been suspended. Were Mr. Putin now to agree to negotiations with the Ukrainian government, it’s likely that no further steps would be taken.

Meanwhile, Mr. Putin has floated another radical measure: Russian annexation of Crimea. The Crimean parliament, which is under Moscow’s control, voted unanimously Thursday to endorse the step and to hold a referendum March 16. In Moscow, Russian parliamentarians quickly began preparing legislation to tuck Crimea into Russia, even as pro-annexation demonstrators flocked to Red Square.

The threat quickly got President Obama’s attention, and for good reason. No country has invaded and then annexed part of a neighbor since Saddam Hussein’s Iraq sought to swallow Kuwait in 1990. No such land grab has happened in Europe since the 1930s. A Russian annexation of Crimea would be an extraordinary violation of international treaties and the U.N. Charter. If tolerated by the world, it would open the way for aggression by many other powers with claims on their neighbors, including China.

Mr. Putin, however, has a fallback. The Crimean parliament authorized a second option, the revival of a short-lived 1992 constitution that declared Crimea to be an independent state within Ukraine. That would be an unacceptable outcome for Ukraine, turning the region into a separatist puppet state such as those Russia already controls in Georgia and Moldova and creating another “frozen conflict.” But to Europeans and the Obama administration, it might look reasonable compared with annexation.

The Obama administration and European Union are right to seek a diplomatic settlement of the crisis. The danger is that they will be bluffed by Mr. Putin into settling for the unacceptable — Russian annexation or de facto annexation of Crimea — without imposing penalties that would exact a meaningful cost and deter further aggression. Some argue that the West lacks the means to damage the Putin regime or that the United States cannot act without Europe, but neither claim is true. Banking sanctions — denying Russians and their banks access to the U.S. financial system — could deal a powerful blow. Mr. Obama must respond to Mr. Putin with measures that force the Russian ruler to rethink his options.