Moscow (CNN) -- Russia's tactics in Ukraine are difficult to pin down: The Kremlin categorically denies Russian troops are fighting alongside rebels there, or that the sophisticated weaponry being used against Ukrainian government forces is supplied by Moscow.
In fact, there's mounting evidence of both.
NATO has released compelling satellite imagery -- dismissed by Moscow -- purporting to show Russian forces crossing the Ukrainian border.
Last week, the Ukrainian military even captured 10 Russian paratroopers inside Ukraine.
The Kremlin said the troops had accidentally crossed from Russia while patrolling the long, porous border that separates the 2 former Soviet states.
But while questions about Russia's tactics remain, its strategy has become more clear: The Kremlin appears to have decided to prevent Ukraine turning West and leaving what Russia regards as its sphere of influence.
That means denying Ukraine membership of Western institutions like the European Union, and NATO.
What's more, the Kremlin appears determined to achieve its goal regardless of the cost.
International sanctions imposed on Russia so far have damaged the country's economy, sending the Ruble to all-time lows against the US dollar, but have had little impact on Kremlin policy.
President Vladimir Putin continues his support of the rebels in Ukraine, even increasing it, according to Western officials.
And he continues to enjoy soaring popularity, with approval ratings of well over 85%, according to opinion polls.
How to stop Putin and prevent a descent into all-out war, then, is the central question with which Western officials are now grappling.
There's talk of further "costs and consequences" -- the words of President Obama -- but there's division on what further sanctions can achieve.
Taking the World Cup away from Russia, chosen to host the next event in 2018, is being discussed and may send a powerful symbolic message of isolation to Moscow. But few expect it would force the Kremlin to change course.
Further economic sanctions would be double-edged, and may work no better than similar previous measures.
NATO, the Western military alliance, is meeting this week in Wales and will examine what its response to Russia should be.
Ahead of the meeting there's talk of increased military support for Ukraine, and that may yet be delivered; but direct confrontation with a nuclear-armed Russia is regarded by member states, including the EU, as a non-starter. It's simply too risky.
President Putin himself summed it up in a speech to a pro-Kremlin youth camp outside Moscow last week, voicing what many of his Western counterparts may well be thinking.
"It's best not to mess with Russia," he said. "Let me remind you, we are a nuclear superpower."
That just leaves diplomacy, so often the last and best option.
The good news is that the Russian and Ukrainian presidents met last week for the first time since June.
The bad news is that there was only an awkward handshake at the summit in Belarus, and a refusal by either leader to compromise.
Russian wants a ceasefire to freeze the conflict, and ultimately a federal constitution in Ukraine that would grant Russian language official status and Russian-speaking areas of the country greater autonomy.
Ukraine rejects this, fearing it would mean losing effective control of its Eastern provinces for good.
That deadlock will simply have to be broken if this Ukraine crisis is going to end without further bloodshed or territorial losses.
EU officials say it's still not too late for Russia to end the crisis without losing face.
But with Moscow so clearly digging in its heels, it may be the government in Kiev and its Western backers who, despite the bluster, will be looking to do a face-saving deal.