I use a backpack (a decent sized pack that can carry as much as a rollar) and a small computer bag.

Only questioned once in my last 10 years. If need be I have all my valuable (and useful onboard) items in the small hand held. And If they accept the backpack but insist on one, I can quickly stuff the bag in the pack (unless this is a long overseas trip when it will not fit).

I prefer to be ready for whatever they insist on, vs trying to fight it.