Who will be the next CEO of Chipotle?

Speculation about who’ll become the next CEO of Chipotle Mexican Grill is well underway. Hours after current chief Steve Ells resigned, members of the online investment community SeekingAlpha.com were already postulating that Ron Shaich, the current CEO of Panera Bread Co., would be an ideal fit. He’ll be out of a job by choice as of Jan. 1, and he’s been a hardcore advocate of transparency, simplicity, wholesomeness and many of the other attributes that made Chipotle a standout.

We don’t think that will happen. If there’s a sharp turn in Shaich’s career, we think it will be into politics.

But a fit of who’s-next guessing is too delicious to be ignored. Here are some of the candidates who should at least merit an interview with the screeners looking for Ells’ successor.

A current director of Chipotle, Paull also has ties with Pershing Square, the investment fund that likely pushed behind the scenes for Ells’ departure. Pershing is one of Chipotle’s largest shareholders, and principal Bill Ackman has flatly said the chain is undershooting its potential by ignoring opportunities like international expansion and breakfast. Paull, an advisory director for Pershing, has Ackman’s ear, and vice versa.

He has the added advantage of a financial background. Ells was a chef-turned-CEO. Paull was the CFO of McDonald’s—during the time when Chipotle was owned by the burger giant, and McDonald’s international operations were the company’s bright spot.

The downside: He doesn’t have the operational chops that Chipotle likely hopes to find in a new CEO. Operational savvy, hardcore business sensibilities and proven business development skills appear to be the essential needs, and Paull brings only two of the three.

She and Chipotle are like the two unescorted single people at a dinner party of couples. Why not get together? Bachelder hasn’t had a regular job since stepping down as CEO of Popeyes Louisiana Kitchen when the chicken chain was sold to Burger King’s parent, Restaurant Brands International. And Chipotle has an opening for someone who can turn around an ailing limited-service brand. Popeyes was colder than two-day-old chicken when Bachelder took the helm. It was sold a few years later for $1.8 billion.

Wall Street knows the story well. Bachelder developed a full narrative when the repair of Popeyes began, setting out six principles and then studiously working the program. Investors got it. They couldn’t always say the same about Chipotle’s plan.

Still, the glove is a rough fit in some ways. One of Bachelder’s strengths is working with franchisees. All of Chipotle’s restaurants are corporately run.

She’s also worked solely in the fried-chicken segment, at KFC before Popeyes. Chipotle has literally mocked operations like those, to the merriment of customers. Would that undercut the chain’s perception as a disruptor?

Chipotle is much different in scope, volume and reputation from Reddy’s former charge, the Noodles & Co. fast-casual chain, which he led for 10 years. But Reddy in many respects has an ideal background. He worked several decades for McDonald’s, starting as a cook and rising into senior executive levels, with exposure to everything from international operations to real estate, finance and marketing.

He also knows how Chipotle functioned in better days. Reddy was reassigned to the chain when it was still owned by McDonald’s. He joined Ells and the startup team when Chipotle had only 13 units open. Serving in a variety of roles, including chief operating officer and chief operations officer, he helped grow it to 420 units before leaving for Noodles.

Plus, he’s lived a good part of his life in Colorado, the home state of Chipotle.

The fast-food veteran retired less than two years ago, having served most recently as CEO of Wendy’s. But his skills align so precisely with Chipotle’s needs that a headhunter should be banging away on the phone in hopes of getting the parties together.

Chipotle is all about better food and a different limited-service experience. Those were the pillars of the turnaround Brolick engineered for Wendy’s.

He’s also strong in menu development and operations, two areas Chipotle has readily admitted are weaknesses. Between two lengthy stints at Wendy’s, he worked at Taco Bell, where systems, value, guest frequency, concept evolution and other shortcomings of Chipotle were all key points of focus.

And Brolick is only 69 years old.