Every year beginning in November, the tawny, mottled birds known as houbara bustards make their annual migration southwest from their breeding grounds in Kazakhstan, China, and Mongolia. Most end up in the deserts of Pakistan.

Another migration, by some of the richest and most powerful men in the world, soon follows them there, armed with almost every kind of hunting weapon imaginable.

Well, no drones, so far. But for Pakistani environmentalists, this uncontrolled slaughter by foreign powers is almost as enraging. The hunters often deploy a trained falcon to swoop in on a houbara and slam it to the ground, the victim reduced to a violent flapping of wings and feathers torn loose from its flesh. (They preserve the memory in videos like this.) They also use shotguns on houbaras and target Siberian cranes and almost any other living thing foolish enough to come in range. A 2011 estimate—a guesstimate, really—put Asia’s houbara population at no more than 55,000 birds and sharply declining.

The houbaras, as well as the cranes, are nominally protected under the Convention on International Trade in Endangered Species, and the hunters all come from countries that are signatories to that convention. Worse, many of them are heads of state or national leaders of those countries—among them the United Arab Emirates, Qatar, Bahrain, Saudi Arabia, and Kuwait. This year, UAE actually sent a large delegation to slaughter bustards in Pakistan while it was simultaneously signing a treaty to protect them in Kazahkstan. (The apparent aim is to protect the birds for future hunting.)

You can find a complete list of the permit holders for the latest hunting season, which took place in December and January, here. It might be worth paying attention to the names, because these otherwise powerful men apparently hunt at least in part to boost their sex lives: Tradition says that the aphrodisiacal flesh of houbaras ranks somewhere between Spanish fly and Viagra. Maybe it’s a kind of sympathetic medicine, suggested by the long, upright necks of these birds. But it takes a lot of houbaras: Each of the 33 permits issued this hunting season allowed the holder to take 100 birds. Critics say the reality is that the hunters kill indiscriminately.

"Is there any more ridiculous reason to kill an animal?" asks Naeem Sadiq, one of the activists whose petition to end the hunting succeeded in establishing an interim ban last week while the case proceeds. Pakistan has also warned the sheiks that it plans to suspend the 2014–15 season, to allow for recovery of the birds. But environmental critics are skeptical that it will follow through. "If it's illegal for Pakistanis to kill these birds, why should the Arab sheikhs be allowed to do it?" Sadiq says.

The short answer is that they have money. The sheiks spend lavishly not only on the private jets and transport planes (along with cooks, drivers, cleaners, and other staff) needed to set up luxurious hunting camps but on improving local roads, runways, and schools in Sind, Punjab, and Balochistan, the provinces where most of the hunting takes place. Their benefactions may also matter on the national level. During the 2012–13 hunting season, Pakistan’s then president, Asif Ali Zardari, invited the son of Qatar’s prime minister to hunt inside his country’s second-largest national park. (Zardari now faces graft charges, apparently unrelated to the bustard hunting.)

Officials in Sind have challenged the Ministry of Foreign Affairs' right to issue hunting permits, with one provincial official promising that if it regains its constitutional rights, “we will immediately introduce a five- or 10-year ban because the bird numbers have become so low." (It’s not the first time regional authorities have protested against a national government’s decision to allow indiscriminate hunting by Arab sheikhs. The same thing happened in the African nation of Niger in 2003.)

“Very soon we will be left with nothing—no wildlife, no biodiversity,” says Ali Murtaza Dharejo, a zoologist at the University of Sindh. “We are destroying the natural habitats of the birds and the animals; there is no vegetation, fewer ponds, and hardly any weeds left.”

India has already banned the houbara hunt. The question is whether Pakistan will step up to the example set by its regional archrival. Pakistan’s Save the Houbara group has a Facebook page. World Wildlife Fund’s Pakistan branch is also active on the issue. But given our own bloody reputation in that country, Americans' help may not be particularly welcome.

So here’s another idea: Check out this year’s hunting permits, and post each hunter’s name on Twitter—and add a friendly offer to send him a lifetime supply of Viagra, if he will just leave the houbaras alone.