From the company that used to offer "the friendly skies"

United Continental Holdings Inc will become the first big U.S. airline to limit low-fare customers to one carry-on bag that fits under a seat...
United, the No. 3 U.S. airline by passengers carried, said customers who bought its cheapest fares would not be assigned seats until the day of departure, meaning people on the same ticket may be split apart.
United will also prohibit these travelers from carrying on bags that can only fit in overhead bins, and they will not accrue miles toward elite status.
The company expects the moves to add $4.8 billion to its annual operating income by 2020, although the figure does not include rising wages.  Fare initiatives such as "basic economy" will account for $1 billion of this, as more customers pay to check bags or select higher fares that give them two "free" carry-ons.

The classic rolling carry-on, of course, does not fit under a seat.  More at Reuters.