How much will an airline pay you to give up your seat? The answer: As much as you can negotiate for.

By law, the airlines do not have to pay more than 400% of the value of the ticket, up to $1,350, when they bump someone off a flight against their will.

But airlines occasionally offer more than that to find a volunteer.

United Airlines says it offered $1,000 to a passenger on Sunday before he was dragged off a plane, screaming and bleeding, to make room for a commuting crew member who needed a seat. Other passengers say the compensation offer stopped at $800.

Since then, of course, United has taken a costly public relations hit. And its stock lost $250 million in value on Tuesday. After two days of growing outrage and two statements that only seemed to make things worse, United CEO Oscar Munoz finally apologized on Tuesday and called the episode "truly horrific."

United declined to explain why it didn't offer more, or talk about its guidelines for negotiating with passengers. The airline said that would be part of its review of what went wrong in Chicago.

Related United CEO apologizes for "truly horrific" passenger incident

Laura Begley Bloom and her family had a better experience last week. Delta paid them $11,000 not to fly.

Begley Bloom, her husband and her 4-year-old daughter had tickets to fly from New York to Fort Lauderdale, Florida, on Friday. It was the third day of the Delta weather debacle, and thousands of unhappy passengers needed to be rebooked.

So Delta was offering top dollar to anyone who would agree to give up a seat.

When the gate agent offered $900, Begley Bloom's husband offered their three seats for $1,500 each. The agent countered with an offer of $1,350 apiece -- so the family left the airport with $4,050 in vouchers and a promise that they would be put on a flight on Saturday.

Two of them were feeling pretty good about things.

"I'm not going to lie to you, my daughter cried. She was upset not to see her grandparents and cousins," Begley Bloom, a travel editor who now runs a consulting business, told CNNMoney.

"But we weren't sure that flight was ever going to leave," she said. "There were people who were at the gate who had been sleeping on the floor for days, yelling and cursing. We just wanted to get her away from there."

Related: Buckle your seat belt. You're stuck with your airline

When the family returned to the airport on Saturday, they found the flight overbooked once again, and gate agents looking for more volunteers. They left with $3,950 more and a promise that they would be put on a flight on Sunday.

But the third day was no better. They agreed to have their tickets refunded and accept an additional $1,000 per ticket.

"I've been a travel editor for 25 years," Begley Bloom said. "I've been on plenty of flights where they asked for volunteers. I've never done it."

What gate agents are willing to offer depends more on the situation than on the airline, said Robert Mann, the head of airline consulting firm R.W. Mann & Company. It boils down to "how badly they need volunteers" and how willing customers are to accept other flights, he said.

Brett Snyder, a former airline executive and editor of the travel blog Crankyflier.com, said it's rare for airlines to offer more than $1,350 for a voluntary seat surrender, but he's heard of it happening.

"Sometimes you're just desperate to find the passengers who agree to be bumped, like United should have been," Snyder said. "It would have saved them a lot of money if they had offered more."

--CNNMoney's Julia Horowitz and Jon Ostrower contributed to this report.