“He’s usually between her legs. She pets him a lot,” said Halama, a Chicago-area sales executive who flies frequently and often takes her daughters and Ollie. “If this goes through, we’re going to have to drive everywhere.”

The proposed rules seek to address conundrums that mushroomed as more animals have taken to the skies, the most controversial of which may be the proliferation of emotional support animals. Training is not required for support animals, about 751,000 of which flew in 2017.

The current regulations’ broad definition of a service animal has allowed all manner of species to board free — a duck and a marmoset among them — and drawn ire from airlines and organizations that train and partner service dogs, which say untrained creatures undermine and imperil skilled animals with jobs.

Along the way, the phrase “emotional support animal” has become code for the entitled excesses of a pet-obsessed society.

“The days of Noah’s Ark in the air are hopefully coming to an end,” Sara Nelson, president of the Association of Flight Attendants-CWA, said in a statement.

Although wacky animals get the most attention, the Transportation Department says the vast majority of emotional support animals on planes are dogs. And those who insist that they depend on the animals to cope with mental-health conditions say the proposal would punish them for the abuses of fraudsters who simply want to skirt pet fees, which can cost more than $125 each way.

“There are many, many people in the mental-health community who feel that those animals can be really important and useful,” said Curt Decker, executive director of the National Disability Rights Network. “The airlines have sort of created this mess with exorbitant charges for people who bring their pets — it’s an incentive for them to cheat. And the disability community gets it in the neck.”

Halama’s daughter sees a therapist monthly and moderates her school course load to help, but Ollie “is like her guiding angel,” Halama said. “She feels like bad things are not going to happen if he’s next to her.”

There should be a system to approve individual domesticated animals, “like TSA PreCheck for dogs,” Halama said. “Bringing a peacock to an airport is not reasonable. Bringing a duck with a diaper is not reasonable. Bringing a sweet, well-behaved mini goldendoodle? That passes the reasonability test for me.”

An animal-vetting system seems unlikely at this point. In addition to allowing airlines to turn away emotional support animals, the Transportation Department’s proposed changes would narrow the definition of a service animal to dogs that have been trained to perform tasks for an individual with a disability — guide dogs, for example. Psychiatric service dogs, which are sometimes trained to act as a barrier between their owners and other people or to turn on lights, would qualify.

An agency official emphasized that airlines could continue to board emotional support animals if they choose. The agency is seeking public comment on the proposed rules until late March, including on whether and how the changes would “impact the ability of individuals with disabilities who rely on emotional support animals to travel via aircraft.”

The study of animals’ effects on people with depression and other mental-health conditions is a relatively young field, and empirical evidence for their therapeutic value remains thin. Still, there is widespread public belief in the mood-boosting power of pets, and individual accounts of comfort from animals are common.

Dailee Fagnant, a graduate student in Oklahoma, said she has five horses, three snakes and two dogs, “but only one of my animals is an emotional support animal.” That’s Belle, a 75-pound Australian shepherd-Catahoula leopard dog mix. Fagnant said she has long struggled with depression and has generalized anxiety disorder that can manifest as extreme insomnia.

So Fagnant, 26, flies with Belle — not because she needs her on the plane, but because without the dog at her destination, she said, “I basically become an insomniac, where I don’t sleep at night. I have really bad dreams.”

Fagnant, who trains horses professionally, said she has worked hard to train Belle. The dog doesn’t bark, ignores other animals in airports and sits silently while Fagnant passes through security, she said.

On the three to four flights she takes a year, Fagnant said, she requests a bulkhead seat so Belle has plenty of room. She also asks passengers in her row whether they mind sitting near a dog, she said. “I don’t take it for granted that everyone likes dogs,” she said. No one has ever complained, she added.

Fagnant carries a letter from her psychiatrist attesting to her need for Belle. But one catalyst for the change is the ease with which people can get such letters or an emotional support animal “registration” — even for such absurdities as a beehive or a beer. Airline employees are loath to question such documentation for fear of violating current regulations, their advocates say.

CertaPet, an online company that helps travelers obtain letters from therapists, has pushed back against the Transportation Department’s proposal. Its website prominently touts its service as a way to “Save 100s in Unfair Pet Fees,” and it says it has served 65,000 people. But Prairie Conlon, the company’s clinical director, insists it doesn’t just hand out the letters.

Only about 30 percent of people who take the site’s online “pre-screening” get through to a longer questionnaire, she said. Those who complete it are referred to a therapist in their state who conducts a phone call to determine the person’s need for an emotional support animal — only dogs, cats or rabbits, she said.

Solutions to fake letters from “so-called online telehealth” outfits, Conlon said, could include some sort of federal regulation of the sites and training for clinicians and physicians on animal-assisted therapy.

“Emotional support animals are kind of part of this holistic movement. We’re trying to get away from the medications, and you’re seeing a lot more of the yoga, meditation and mindfulness,” Conlon said. “It’s a very natural and consistent daily form of treatment.”

The agency’s proposal, which followed years of deliberations and thousands of public comments, does not appear to see it that way. Fagnant said she can understand why. The rules need to be tightened, she said, to keep unvaccinated animals and unusual species out of the cabin. Just how, she’s not sure.

“I do the right thing, so it’s hard for me to speak on behalf of people who don’t,” she said.

If the rule is finalized, she said, “I wouldn’t fly anymore.”

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