One can only cheer at what now seems to be the removal of Muammar al-Qaddafi from power, at the hands of his own long-abused people. And one must commend the NATO special forces and air power — particularly from Britain, France, and the United States — which helped bring about this outcome.

As a young diplomat, I spent Christmas 1988 sleeping in a makeshift office in a high school chemistry lab in Lockerbie, Scotland, as we worked around the clock to help police identify the remains of the nearly 200 Americans killed on Pan Am Flight 103. I was aware of the brutality of Qaddafi’s regime at home and saw firsthand his willingness to use terrorism abroad. Thus, despite Qaddafi’s temporary thaw with the West during George W. Bush’s administration, I was not particularly surprised by his callous and brutal determination to stand in the way of the revolutionary moment sweeping the Middle East — the best hope for millions of Arabs in a generation.

I was appalled when Scottish authorities released the Lockerbie bomber, Abdelbaset al-Megrahi, from prison in 2009. And I took personal satisfaction in seeing the images from Tripoli during the past couple of days, as Qaddafi’s regime seemed to finally be coming to an end.

But take it from a die-hard Atlanticist: Despite this good outcome, it would be a mistake to chalk this up as a success for NATO. Indeed, it is more accurate to say it is a success despite deep-rooted problems that still remain unaddressed within the alliance.

The problems began with the definition of the mission itself and have extended right through NATO’s leadership, execution, and that most tenuous of all assets, solidarity. NATO must be careful to avoid a round of self-congratulatory back-slapping right now; it needs to tackle all these problems systematically if it is to remain a credible military alliance for the future.

The mission problem: NATO defined its mission in Libya as protecting civilians and humanitarian relief. But even the most casual observer concluded (as I did five months ago) that there was no way to protect civilians so long as Qaddafi remained in power. And though NATO did strike some central command installations in the heart of Tripoli, killing some members of the Qaddafi family, the alliance had explicitly ruled out “regime change” as a goal — so for several months, there was a distressing lack of seriousness of military purpose.

This changed in recent weeks as Britain, France, and Italy (with U.S. support) put special forces advisors on the ground, provided equipment, established tactical communications and intelligence cooperation with the rebel forces, and coordinated NATO air attacks with rebel advances. But these decisive efforts took place despite the official NATO mission, not because of it. And as long as it worked, more squeamish allies could look the other way.

So why did NATO adopt a halfway mission in the first place? Because NATO can only make decisions by consensus, and Germany and Turkey, among others, opposed a more robust mission. The U.N. Security Council only authorized protection of civilians, and these allies wanted NATO to go no further than what the council had approved. Germany, for its part, actually removed four of its warships from the Mediterranean, lest they were somehow to get embroiled in the fight.

During Bill Clinton’s administration, I worked on NATO’s 1999 Strategic Concept, in which the United States fought hard to avoid linking NATO military action to explicit U.N. authorization. But in 2011, this linkage was made in practice — in effect allowing Russia and China to use the U.N. Security Council to set the limits on NATO action in Libya.

Beyond the U.N. issue, however, lies a deeper problem — the discomfort many European allies have with the exercise of military force. Robert Kagan wrote extensively about this postmodern idealism in Of Paradise and Power. European military establishments, he wrote, are from Venus. They are extolled for such things as “protecting civilians,” “peacekeeping,” “delivering humanitarian relief,” and “providing stability.” But what about Mars — actually using the military for its principal purpose: defeating an opponent by overwhelming force? That is unpalatable for many European allies. Yet without it, what does it mean to have a military alliance?

The leadership problem: Compounding the confusion from the muddled mission was a confusing message about alliance leadership. After playing a major role in the initial wave of airstrikes, the United States abruptly pulled back from the mission, saying — in the words of President Barack Obama — that Washington was “handing over to NATO” the operational lead.

To be sure, this washing of hands was due to domestic political considerations, including public fatigue with two other wars, Tea Party anger at an out-of-control Washington, and massive budget pressures. But the United States has long been the leader of NATO, so speaking of the alliance as if America is not in it — as a “them” — felt particularly jarring. It sent a confusing message back in Washington, because despite this declaration, the United States continued to put airmen and sailors in harm’s way by providing substantial noncombat support as part of the NATO operation. Why put American men and women at risk if the United States was not seeking a strategic outcome and if Europeans were supposed to be doing the work, not Americans?

Ironically, the tendency to think of NATO as “them” has long been the pattern in Europe, where NATO is often synonymous with “the Americans.” So when both the United States and Europe think of NATO as “them,” who exactly takes ownership of the alliance? Instead of bowing to this trend, both sides of the Atlantic need to reaffirm their own responsibility for NATO if it is to mean anything in the future.

For the United States, there needs to be something in between unilateralism and “handing over” the reins to others. Washington needs to feel comfortable leading together with others, as it did in Kosovo and the Gulf War.

At home, the United States needs leaders willing to make the case for the use of force, define war aims, and earn public support. Instead, the administration found itself fighting a war abroad, yet refused to define it as such because doing so would have upset the self-deception of NATO’s remit to protect civilians, presented more headaches in the United Nations, and given ammunition to domestic U.S. critics who suddenly developed a newfound interest in the War Powers Resolution. It is hard to make the case to the public for why America is fighting — and particularly for why it must win — if the administration refuses to acknowledge the country is engaged in hostilities.

The execution problem: Years of European countries hollowing out their defense budgets — even while taking part in an expensive operation in Afghanistan — demonstrated that the majority of European allies now lack the capabilities to take on even a basic military mission such as a no-fly zone without the United States. One of the most capable allies, Britain, is facing an 8 percent defense budget cut and was running out of precision-guided munitions after a few months of operations. Several British commentators have questioned whether, given budget trajectories, the country could afford to do again a few years from now what it is doing in Libya today.

The United States, meanwhile, withheld assets from the mission — such as A-10 anti-tank aircraft and, in early days, Predator drones — when they would have made a substantial difference.

Yet it was a good decision to leave the fighting on the ground to the Libyans themselves rather than send Western ground troops. After all, they stood up to their dictator, and they were willing to fight for their country. And soon they will be able to claim that success is theirs and theirs alone.

But NATO held out far too long before imposing the no-fly zone — by which time Qaddafi was on the verge of routing Benghazi and had already shifted tactics. And coalition allies held out far too long before giving the rebels intelligence, communications, special forces advisory teams, equipment, and tactical air support. All this could have been done within a few weeks of the outbreak of fighting. In the end, certain allies did it anyway, though under the table and on their own recognizance, rather than as NATO. It worked, but at a greater cost in lives and treasure than might have been the case.

The solidarity problem: The concept of an alliance is one of sharing common strategic purposes and being willing to fight together for the common good. Take NATO’s Article 5 commitment to collective defense: all for one and one for all, hang together or hang separately — all that stuff.

This solidarity was already severely damaged by the war in Afghanistan, when despite having agreed to a NATO mission, several allies then put caveats on the use of their forces, such as limiting them to noncombat zones, even when it came to flying medical support missions. This is understandable because each government must face its own domestic politics — but it’s also destructive of the alliance as a whole. Even so, the United States worked hard and successfully made the case that because Afghanistan is a NATO mission, every NATO ally must contribute in some way. And each one did.

But if solidarity started fraying in Afghanistan, in the case of Libya it went out the window. Several allies did not take part at all — in some cases because they lacked relevant capabilities, itself a blemish; in others because they chose to limit their roles to zero, or inconsequential elements of the mission.

And the United States itself became a caveat country, putting limits on the roles it would play and specific capabilities it would contribute in support of the NATO mission in Libya. No doubt, defenders of the U.S. approach will claim differently — that the United States is leading in Afghanistan, has other responsibilities, and was willing to provide critical, unique combat support assets for Libya. But politically, the United States has now made the case in practice for why caveats are acceptable — and that is a tragedy for NATO as a whole.

None of this is to say that NATO is down for the count. But if we think of Libya as a NATO success story, we will never get to the bottom of the major problems still plaguing the alliance.

And, to be sure, we still need NATO: In a world in which ideological, military, economic, political, and sheer chaotic threats are growing, Europe and North America — these twin pillars of democratic values in the world — need to act together more closely than ever before.

But to restore NATO to its position as the world’s preeminent military alliance, which it was and which it should be, we need to make a realistic assessment of the problems that the Libya operation exposed and work hard to overcome them before the next time NATO’s capabilities are needed.

Kurt Volker, a Senior Advisor to the International Security Program and member of the Atlantic Council’s Strategic Advisors Group, is a former US Ambassador to NATO.  This essay originally appeared on Foreign Policy.