Last weekend America announced that it was sending more troops to Iraq, Russia allegedly sent more troops into Ukraine and President Barack Obama set off for Beijing.
Ask policymakers in Washington which of these parts of the world should be America's top priority and the first response is usually a variant of - "We've got to be able to chew gum and walk at the same time." Press on, and the replies get more interesting.
Broadly speaking, the Washington consensus seems to be that, of the two immediate crises, the one in the Middle East is more urgent than the one in Ukraine. One US national security official, whose responsibilities include both Russia and the Middle East, looked incredulous when I asked him, last week, which was the more important: "The Middle East, by far," he replied.
The argument for prioritising the Middle East is threefold. First, there is an actual war going on, with the United States involved in daily bombing raids. Second, if national security is defined as protecting civilian populations from harm, the Americans see a much more immediate threat from jihadist terrorism than from Russia. Third, the Americans believe an entire regional order is unravelling in the Middle East and that the reordering could take decades. By contrast, the order in Europe is only fraying at the edges.
Some even worry America's preoccupation with Russia distracted its attention from Iraq and Syria, at a vital time. One official muses: "I do wonder whether historians will record that, in the spring of 2014, we were too focused on Ukraine, just as (ISIS) was grabbing control of huge swathes of territory."
The phenomenon of policymakers looking in the wrong direction is not unknown in history. In the month before the outbreak of the First World War, the British government spent far more time discussing the prospect of civil conflict in Ireland than the threat of war in Europe.
But for those who worry most about Mr Vladimir Putin's Russia, it is the Middle East that is the dangerous distraction. The "Russia first" crowd is stronger in Warsaw and Berlin than in Washington. It worries that the US has been drawn back into the "war on terror" and the conflicts of the Middle East, just as the dangers in Europe are mounting.
According to this analysis, the US has still not recognised the radicalism of the challenge posed by Russia. The annexation of Crimea and incursions into eastern Ukraine are, it is feared, just the start. At some point, Russia is likely to threaten more of Ukraine, or even the Baltic states. The very fact that America has ruled out military action over Ukraine has inadvertently raised the stakes. As one senior European diplomat puts it: "Putin knows that he can always escalate to places we won't go."
The darkest scenarios include Russian escalation up to and including the use of tactical nuclear weapons. If that were to happen it would be the biggest international security crisis in decades - far more significant and dangerous than another round in the 25 years of fighting in Iraq.
Most experts still dismiss the nuclear scenarios as far-fetched. It is more common to worry that Mr Putin may launch an all-out conventional war in Ukraine - or encourage uprisings by Russian speakers in the Baltic states, which are members of Nato. If Russia then intervened in the Baltic states and Nato did not respond, the Kremlin would have achieved the huge prize of demonstrating that the Western military alliance is a paper tiger.
Some hope that the growing pressure on the Russian economy and the rouble might dissuade the Kremlin from escalation. But an economic crisis could also make Russian behaviour more unpredictable and reckless.
Amid all this angst, Mr Obama set off for a summit in China. For believers in America's "pivot to Asia" it remains true that - over the longer term - the biggest challenge to US power is still a rising China, rather than a declining Russia or a disintegrating Middle East. They worry that the more the US gets sucked into the crises, the easier it will be for China to achieve primacy in East Asia - the region that is increasingly the core of the global economy.
The Obama administration is determined that this will not happen, and is shifting US military resources so that in future, 60 per cent of the American navy will be based in the Pacific. It will be up to historians to decide whether the Obama administration got its strategic priorities right, or whether it charged off in the wrong direction at a crucial moment.
My own instinct is that Russia is now the most important challenge. The rise of China is hugely significant but it feels like a long- term process - without immediate risk of conflict with the US.
Failing states in the Middle East and the risk of terrorism are dangers that feel almost normal.
But an angry, nuclear-armed Russia, intent on challenging US power, poses risks that we are only beginning to understand. Peace in Europe may depend on Washington striking exactly the right balance between deterrence and diplomacy.