Setara Qassim said a flight attendant confronted her during the trip from Tucson, Ariz., to Burbank, Calif., and asked whether she had a sweater to go over her green halter-style dress.
Qassim, 21, told KNBC-TV in Los Angeles she was forced to wrap a blanket around herself for the rest of the flight. She complained that if Southwest wants passengers to dress a certain way, it should publish a dress code.
Last week, 23-year-old Kyla Ebbert said a Southwest employee pulled her aside as she was preparing to board a plane departing San Diego for Tucson in July and told her she was dressed too provocatively to fly.
Ebbert, who took her case to NBC's "Today Show," said she was allowed on the plane after adjusting her sweater and short skirt. She said she was humiliated and felt the stares of other passengers who had overheard the verbal dressing-down.
Dallas-based Southwest Airlines Co. acknowledged the incident involving Ebbert, but airline spokesman Chris Mainz said the company had no record that Qassim ever complained.
Messages left with Qassim at her California home were not immediately returned to The Associated Press.
Southwest - which dressed its stewardesses in hot pants and called itself "the love airline" back in the 1970s - relies on employees to decide whether a passenger's attire may offend other customers, Mainz said.
"We don't have a dress code. We rely on our employees to use common sense, good judgment and good taste," Mainz said. "It's so rare for us to have to address a customer's clothing issue."
American Airlines claims the right to refuse to carry passengers for a variety of reasons, including being drunk, barefoot, having an offensive odor or being "clothed in a manner that would cause discomfort or offense to other passengers."
"It's generally a graphic on a T-shirt that might be uncomfortable" to another passenger, said American Airlines spokesman Tim Wagner. "We always find ways to mitigate it as best possible, with not allowing someone on a flight being the last option."
David Castelveter, spokesman for the Air Transport Association, the trade group of the major U.S. airlines, said he didn't know of any airline having a dress code for passengers.
Lynda White, who teaches etiquette classes and calls herself "The First Lady of Manners," said many young people have gotten lax on what to wear and how to act - possibly influenced by Hollywood stars. She recommends "business-casual" outfits for the plane because you might be seated next to a potential employer or business contact.
"If you wear provocative clothing, tattoos, or you smell of alcohol or cigarettes, who's going to believe you?" she said.