Investors fled Abercrombie & Fitch yesterday, causing the stock to plunge 20%, after the company reported lower sales and a downbeat outlook. This is where I would normally mention the CEO’s name in boldface, but I can’t — because Abercrombie (ANF) has no CEO.

In fact, it hasn’t had one since December 2014, when founding genius Mike Jeffries resigned suddenly as his magic touch abandoned him. The company sought a successor for a while but seems to have settled into life without one. Intriguingly, it isn’t the only company to operate that way, raising the question of just how much leadership a company really needs.

See also: So Much for Abercrombie & Fitch’s Comeback

Abercrombie’s recent poor performance doesn’t nail the case against the CEO-free organization. Just last fall the company reported knockout results that pushed the stop up 25% in one day. CNBC’s Jim Cramer marveled, “You would think that Abercrombie would be directionless with no one at the helm, but you would be wrong.” The place is being run by executive chairman and retail veteran Arthur Martinez, 76, and a small group of executives.

Everyone knows Abercrombie, but you’ve probably never heard of Morning Star. It’s the world’s largest tomato processor, handling 25% to 30% of all the tomatoes processed in America, and it does so with no bosses, no titles, and no promotions. It has been doing this with tremendous success for 46 years. Consultant and author Gary Hamel “discovered” the company and revealed it to the world.

Or consider DPR Construction, which has appeared multiple times on Fortune’s ranking of America’s Best Companies to Work For — again, no CEO. Maybe you recall Ricardo Semler radically transforming his family’s business in Brazil over 20 years ago by (among many radical changes) passing the CEO title around among top managers every six months.

All those companies have performed extremely well. So is CEO-free Abercombie onto something big and merely going through a bad patch? I don’t think so. Those other companies are all privately held, and, more important, all were built from scratch by one or more driven leaders who believed passionately in their anti-hierarchical visions. Paradoxically, it was only through powerful leaders that these companies could learn to work well without a CEO.

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In most other companies, with more traditional cultures, it’s just the opposite: Only when one person feels the full weight of responsibility for performance can it perform at its best.

Memo to the Abercrombie board: Maybe it’s time to revive that CEO search.