DALLAS – Airlines give many reasons for refusing to let you board, but none stir as much debate as this: How you're dressed.

A woman flying from Las Vegas on Southwest this spring says she was confronted by an airline employee for showing too much cleavage. In another recent case, an American Airlines pilot lectured a passenger because her T-shirt bore a four-letter expletive. She was allowed to keep flying after draping a shawl over the shirt.

Both women told their stories to sympathetic bloggers, and the debate over what you can wear in the air went viral.