The city of Taiz illustrates the complexities. The Saudi bloc in 2016 broke through a Houthi siege of Yemen’s third-largest city with the help of local Salafists, members of a revivalist Islamic school that underpins the religious thinking of groups like Al-Qaeda and Islamic State. With other coalition-backed forces and equipment, they carved out a corridor from the city’s southwest. Stability didn’t follow.

Instead, parts of Taiz fell under the control of Al-Qaeda in the Arabian Peninsula (AQAP) until earlier this year and remain a battleground for rival militias, according to local residents.

The rise of extremist Salafists, and the general proliferation of armed groups, is “creating a situation where there’s a huge risk of a conflagration,” said Adam Baron, visiting fellow at the European Council on Foreign Relations in London. “Even if the Houthis disappear from the picture, it’s pretty hard to put that cat back in the bag.”