As Bob says, we women are allowed a handbag in addition to our one piece. But I will admit that some women's idea of a handbag would allow a kitchen sink to be carried around with them.

I occasionally have fragile items that I wouldn't trust to the hold or an extra small bag and little time to wait at the other end. I tend to ask nicely at check-in whether it would be OK to have an extra one - and if it's a quiet flight, they're usually fine about it. I also work on the principle that if I have extra bags, I put them at my feet to avoid using a fellow passenger's overhead space.

I would also agree with the post saying - don't make it look heavy and they won't bother weighing it! If you can hold it out at arm's length while lifting, they're generally fine - it just means more time at the gym!