It just might work. Wednesday’s departure of Yemeni President Ali Abdullah Saleh, the fourth longtime Mideast dictator to fall this year, may lead to success where other Arab Spring uprisings have so far yielded disappointing results.

UN official Jamal Benomar this week managed to get Saleh to sign the dotted line on an agreement to end his 33-year tyrannical rule, send him to New York for medical treatment and (much to the chagrin of the people who overthrew him) give him immunity from future prosecution.

Arab and US diplomats cajoled and threatened, but it took Benomar’s dedication and nuanced diplomacy to finally bring the wily Saleh and his political rivals to Riyadh, Saudi Arabia, on Wednesday. There they signed a detailed agreement to initially transfer powers to his deputy, who’ll work with a unity government representing all political factions. A new president is to be elected within 90 days and a new constitution finished in two years.

Violence may still end it all, but if the agreement holds, Yemen will move forward and our terror-fighting capabilities will likely remain — even improve

Hours after the signing ceremony, Benomar told me that this pact may succeed because, unlike elsewhere, it’s a “managed transition, a well spelled-out road map” to democracy.

Since January, an astonishing turmoil has shaken the Arab world. At first, it raised tremendous hopes — but then came chaos, fear and increased anger. And (worst, from our point of view) it unleashed Islam’s darkest forces.

It all started in Tunisia, when a fruit vendor set himself aflame back in January, giving voice to millions of hopeless and ill-treated young Arabs. Within weeks the country’s old, currupt and sclerotic tyrant, Zine el Abidine Ben Ali, was gone.

A chaotic process prematurely led to last month’s election, which, as expected, was easily won by the Islamist party, Ennhada — Tunisia’s only organized political force, well financed by the Saudis and Qataris. Its longtime leader, Rachid Ghannouchi, became Tunisia’s most powerful man.

Ghannouchi promised that what attracted tourists (cold beer, liberal beachwear) as well as Tunisian freedoms (women’s rights) will remain. Never mind. Since the elections, Tunisian friends tell me, men and women wait on separate lines at the post office. The easy-going beach culture of yore is on its way out — and that’s only for starters.

Defenders say we shouldn’t fear “moderate” Islamism: Look at Turkey, where it’s totally compatible with democracy. Sorry: Kemal Ataturk’s Western-oriented republic has had nearly a century to evolve. With such entrenched traditions, not even Prime Minister Recep Tayyep Erdogan’s Islamist party can totally wreck Turkey’s democratic values.

No such traditions exist anywhere in the Arab Mideast; they need to be created from the ground up. Tunisia’s Islamists are more likely to follow Iran’s model — where internal oppression and outside aggression lurk just below a surface of thin democratic veneer — than Turkey’s.

In neighboring Egypt, the economy has worsened since Hosni Mubarak’s fall. Even if a democracy-loving leader somehow pops up in Cairo, he or she would likely fail to satisfy the perpetually agitated Tahrir crowds. Western-oriented young Twitterati aside, the Islamists are for now best positioned to take power (perhaps in cahoots with the military) and steer away from any semblance of freedom.

Then there’s Libya. After NATO helped to overthrow Moammar Khadafy, we must watch (on top of all the above trends) the vast arsenal of dangerous weapons he left behind. Oh, and a tribal desert society like Libya’s is almost impossible to monitor.

Islamist extremism, bad economy, tribalism: In various degrees, all will plague each Arab country that shakes off the old order. Think of poverty-stricken, sectarian, chemically and biologically-armed Syria after Bashar Assad. To paraphrase Humphrey Bogart in “The Maltese Falcon,” this is the stuff nightmares are made of.

Regardless, in the long run, the great Arab revolt of the early 21st century will be a good thing — or at least not as bad as the order that has kept Arabs down for centuries, leaving them far behind other societies.

How can we help? Sometimes, as Yemen’s example shows, one tenacious, capable man who speaks the language and understands the culture can make a huge difference. If the United Nations can produce a Jamal Benomar, so can we.