Passengers on U.S. airlines could no longer fly with emotional support animals such as peacocks, alligators, or pigs inside the cabin, under new rules the Transportation Department is proposing.

The proposal, announced Wednesday, is an effort to crack down on flyers who falsely claim their pets are service animals. It would narrow the agency’s definition of a service animal to canines trained to assist a person with a disability, and would exclude pets known as emotional support animals, or animals passengers claim they need for their emotional well-being.

Passengers who lie about their animal could be receive fines or jail time, an agency official said.

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

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Several airlines have altered their policies in recent years in response to a growing number of passengers claiming they need animals for emotional support. Those increased numbers also led to at least two incidents in which passengers were injured, including a man who was mauled by a dog on a Delta Air Lines Inc. flight in June 2017. Delta and United Continental Holdings Inc.now require 48-hour advance notice to travel with an emotional support animal.

Airlines have been required since 1990 to analyze whether an animal poses a direct threat to the health and safety of others, an agency official said Wednesday. Under the new proposal, flyers would be required to complete forms, administered by the Department of Transportation, that attest the animal is well-behaved, healthy, and able to relieve itself in a sanitary way.

Advocates for people with disabilities decried the added paperwork, calling it “discriminatory” and “overly burdensome” for those who need to fly with their service animals. “We acknowledge that some people have misrepresented themselves and their pets as people with disabilities,” Curt Decker, executive director of the National Disability Rights Network, said in a statement. “But it is rare. These proposals are an overreaction.”

Airlines for America, the trade group that represents major U.S. carriers including United, Southwest Airlines Co., American Airlines Group Inc.,and JetBlue Airways Corp., applauded the proposal in a statement.

The agency is more than two years late on issuing the proposal. Under the Federal Aviation Administration Extension, Safety, and Security Act of 2016 (Public Law 114-190), the department was required to issue it by July 15, 2017. The FAA Reauthorization Act of 2018 (Public Law 115-254) directed the agency to issue a final rule by April 5, 2020.