Yesterday afternoon, I tweeted that the Obama administration wasn’t getting enough credit for its measured response to the Ukraine crisis so far, asserting that sanctions were really hurting Russia and noting that “we”—by which I meant the United States—were not directly at war.

Not long after I said that, someone I follow tweeted that he hadn’t seen a compelling explanation of how sanctions are supposed to work in this case. That’s an important question, and one I also haven’t seen or heard answered in depth. I don’t know how U.S. or European officials see this process beyond what they say in public, but I thought I would try to spell out the logic as a way to back up my own assertion in support of the approach the U.S. and its allies have pursued so far.

I’ll start by clarifying what I’m talking about. When I say “Ukraine crisis,” I am referring to the tensions created by Russia’s annexation of Crimea and its evident and ongoing support for a separatist rebellion in eastern Ukraine. These actions are only the latest in a long series of interactions with the U.S. and Europe in Russia’s “near abroad,” but their extremity and the aggressive rhetoric and action that has accompanied them have sharply amplified tensions between the larger powers that abut Ukraine on either side. For the first time in a while, there has been open talk of a shooting war between Russia and NATO. Whatever you make of the events that led to it and however you assign credit or blame for them, this state of affairs represents a significant and undesirable escalation.

Faced with this crisis, the U.S. and its NATO allies have three basic options: compel, cajole, or impel.

Compel in this case means to push Russia out of Ukraine by force—in other words, to go to war. So far, the U.S. and Europe appear to have concluded—correctly, in my opinion—that Russia’s annexation of Crimea and its support for separatists in eastern Ukraine does not warrant a direct military response. The likely and possible costs of war between two nuclear powers are simply too great to bear for the sake of Ukraine’s autonomy or territorial integrity.

Cajoling would mean persuading Russian leaders to reverse course through positive incentives—carrots of some kind. It’s hard to imagine what the U.S. and E.U. could offer that would have the desired effect, however. Russian leaders consider Ukraine a vital interest, and the West has nothing comparably valuable to offer in exchange. More important, the act of making such an offer would reward Russia for its aggression, setting a precedent that could encourage Russia to grab for more and could also affect other country’s perceptions of the U.S.’s tolerance for seizures of territory.

That leaves impel—to impose costs on Russia to the point where its leaders feel obliged to change course. The chief tool that U.S. and European leaders have to impose costs on Russia are economic and financial sanctions. Those leaders are using this tool, and it seems to be having the desired effect. Sanctions are encouraging capital flight, raising the costs of borrowing, increasing inflation, and slowing Russia’s already-anemic economic growth (see here and here for some details). Investors, bankers, and consumers are partly responding to the specific constraints of sanctions, but they are also responding to the broader economic uncertainty associated with those sanctions and the threat of wider war they imply. “It’s pure geopolitical risk,” one analyst told Bloomberg.

These costs can directly and indirectly shape Russian policy. They can directly affect Russian policy if and as the present leadership comes to view them as unbearable, or at least not worth the trade-offs against other policy objectives. That seems unlikely in the short term but increasingly likely over the long term, if the sanctions are sustained and markets continue to react so negatively. Sustained capital flight, rising inflation, and slower growth will gradually shrink Russia’s domestic policy options and its international power by eroding its fiscal health, and at some point these costs should come to outweigh the putative gains of territorial expansion and stronger leverage over Ukrainian policy.

These costs can also indirectly affect Russian policy by increasing the risk of internal instability. In authoritarian regimes, significant reforms usually occur in the face of popular unrest that may or may not be egged on by elites who defect from the ruling coalition. We are already seeing signs of infighting among regime insiders, and rising inflation and slowing growth should increase the probability of popular unrest.

To date, sanctions have not dented Putin’s soaring approval rating, but social unrest is not a referendum. Unrest only requires a small but motivated segment of the population to get started, and once it starts, its very occurrence can help persuade others to follow. I still wouldn’t bet on Putin’s downfall in the near future, but I believe the threat of significant domestic instability is rising, and I think that Putin & co. will eventually care more about this domestic risk than the rewards of continued adventurism abroad. In fact, I think we see some evidence that Putin & co. are already worrying more about this risk in their ever-expanding crackdown on domestic media and their recent moves to strengthen punishment for unauthorized street rallies and, ironically, calls for separatism. Even if this mobilization does not come, the increased threat of it should weigh on the Russian administration’s decision-making.

In my tweet on the topic, I credited the Obama administration for using measured rhetoric and shrewd policy in response to this crisis. Importantly, though, the success of this approach also depends heavily on cooperation among the U.S. and the E.U., and that seems to be happening. It’s not clear who deserves the credit for driving this process, but as one anonymous tweeter pointed out, the downing of flight MH17 appears to have played a role in deepening it.

Concerns are growing that sanctions may, in a sense, be too successful. Some observers fear that apparent capitulation to the U.S. and Europe would cost Russian leaders too much at home at a time when nationalist fervor has reached fever pitch. Confronted with a choice between wider war abroad or a veritable lynch mob at home, Putin & co. will, they argue, choose the former.

I think that this line of reasoning overstates the extent to which the Russian administration’s hands are tied at home. Putin & co. are arguably no more captive to the reinvigorated radical-nationalist fringe than they were to the liberal fringe that briefly threatened to oust them after the last presidential election.

Still, it is at least a plausible scenario, and the U.S. and E.U. have to be prepared for the possibility that Russian aggression will get worse before it gets better. This is where rhetorical and logistical efforts to bolster NATO are so important, and that’s just what NATO has been doing. NATO is predicated on a promise of collective defense; an attack on any one member state is regarded as an attack on all. By strengthening Russian policy-makers’ beliefs that this promise is credible, NATO can lead them to fear that escalations beyond certain thresholds will carry extreme costs and even threaten their very survival. So far, that’s just what the alliance has been doing with a steady flow of words and actions. Russian policy-makers could still choose wider war for various reasons, but theory and experience suggest that they are less likely to do so than they would be in the absence of this response.

In sum, given a short menu of unpalatable options, I think that the Obama administration and its European allies have chosen the best line of action and, so far, made the most of it. To expect Russia quickly to reverse course by withdrawing from Crimea and stopping its rabble-rousing in eastern Ukraine without being compelled by force to do so is unrealistic. The steady, measured approach the U.S. and E.U. have adopted appears to be having the intended effects. Russia could still react to the rising structural pressures on it by lashing out, but NATO is taking careful steps to discourage that response and to prepare for it if it comes. Under such lousy circumstances, I think this is about as well as we could expect the Obama administration and its E.U. counterparts to do.