To us, American Airlines was not a problem. For a while they were the cheapest for in-cabin travel. After the first 30-60 minutes of a long cross-country flight, my daughter would take our Chi out and discretely place her on her lap and she would just lay there for hours and the two would fall asleep. Flight attendants might have seen her once or twice in all the travels and luckily never made a fuss over her being out. She was even taken to the lavatory, again discretely, and back with no one making an issue of it.
Hubie So.Cal .
