WASHINGTON (CNN) -- They're known as "lap babies" -- children under age 2 who fly on their parents' laps rather than in a seat of their own. But when planes go down, babies can be hurled through cabins with hundreds of pounds of force.

The Federal Aviation Administration is considering regulations now that would require babies to be buckled up in safety seats. The problem for parents is that they must purchase an extra seat -- at regular fare -- to accommodate the safety seat. And they have to bring their own safety seat. Lap babies, however, fly free.

At Congressional hearings, parents who have lost young children in air accidents have told their stories.

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"(My baby) ultimately ended up in an overhead storage bin which was now on the floor approximately 15 rows to the rear from where our original seats had been," said Lori Michaelson, who had tried to protect her daughter by holding her tight as the accident happened.

In a 1994 crash in Charlotte, North Carolina, an unsecured baby was thrown across the plane during impact. In Denver in 1987, a baby was crushed against a seat by its parent and died. The parent survived.

But the number of children killed -- who might have survived had they been in child safety seats -- is miniscule. Estimates vary, but over the past decade, less than one child a year has been killed in such accidents, out of up to 20,000 small children put on planes every day.

Given the dramatic scenes of terrible crashes, it's understandable that many parents figure that safety seats won't make much of a difference in a crash.

And several years ago, the FAA was reluctant to burden parents with the cost of buying an extra seat for baby -- reasoning that the added cost would push families away from relatively safe air travel in favor of more hazardous road travel.

Some airlines (in some cases) have reduced-fare seats available for children under age 2. (Children 2 and over must pay full adult fare.) But still, parents aren't buying.

Now the FAA is re-examining its position -- asking the public to decide through policy, not pocketbook, whether a gamble for baby is worth a bargain for parents.