As Saudi-led airstrikes appear to have done little to set back the Houthis in Yemen so far, doubts about the kingdom’s ability to meet its stated objectives in the impoverished Arab country are growing.

Saudi Arabia intervened in Yemen last month at the head of a broad Arab coalition that also includes Egypt, the United Arab Emirates and other Sunni-led countries that see the Houthis as proxies for their regional nemesis, Iran.

The Houthis’ advance on the port city of Aden, where Yemen’s internationally-recognized president, Abd Rabbuh Mansur al-Hadi, had holed up, triggered the military action.

The Houthis first took over Yemen’s capital, Sana’a, in September and have steadily expanded their territory since, abetted by forces loyal to Hadi’s predecessor, Ali Abdullah Saleh. Despite the Arab airstrikes, they still control almost the entire west of Yemen, including the territory of the former North Yemen.

Saudi Arabia and its allies seem determined to drive a wedge between the Houthis, a Shia rebel group from the north of Yemen, and Saleh, whom they forced out of office in 2012 amid fears of an “Arab Spring”-style uprising in the country.

The news agency Reuters reports that the strategy is having some success. Five pro-Saleh military brigades have reportedly defected, one of which is now battling the Houthis in the vicinity of Taiz, a city in the southwest.

Further splits could weaken Saleh and help Saudi Arabia and its allies beat back the Houthis who are engaged in street battles for control of Aden.

The Houthi-Saleh alliance is one of convenience. The former strongman waged six wars against the Shia rebels from 2002 to 2009. According to Reuters, “the group fears the Saudi drive for defections could even see Saleh on Riyadh’s side once again.”

The Saudis only withdrew their support from Saleh in 2012 when he seemed unable to put down an Islamist-inspired uprising that the kingdom considered a greater threat at the time.

Although the Arab coalition justifies its intervention by saying they responded to the Hadi government’s request for help, Saleh’s successor is a weak figure with no power base of his own.

Garrett Khoury writes at The Eastern Project that the fighters opposing the Houthis and Saleh loyalists are less pro-Hadi than they are in favor of independence for the former South Yemen.

The Houthi advance has reignited separatist passions, as southerners see themselves as defending against a northern invasion, just as they were in 1994. The Southern Movement, as it is called, has gone from a civil rights-style group when it was born nearly a decade ago to a military force defending the south. They are not fighting for Hadi. He has little visible support, even in Aden.

It was Saleh who presided over Yemen’s unification in 1990 and a civil war that started four years later when the south tried and failed to secede. Hadi, despite being a southerner, never won the trust of the Southern Movement.

The fact that Saudis nevertheless back Hadi shows the truth of their intentions in Yemen, according to Khoury.

They are not backing legitimacy in Yemen, nor the will of the Yemeni people. They are fighting to keep their proxy in power and keep those that they view as Iran’s proxies out of power.

It’s a fight Iran doesn’t even need to participate in, he believes.

Although Iran has thrown its support behind the Houthis, it did not create the group nor inspired their rebellion.

Timothy Furnish, an Iran expert for the crowdsourced consultancy Wikistrat, argues that the Shia republic is less interested in bringing the Houthis to power than it is in leveraging the “persecution” of Shia for regional influence and delegitimizing the Saudi government.

To that end, as Khoury puts it, all Iran needs to do is “sit back” and “watch the Saudis get themselves ever more deeply involved in Yemen.”