What do you do with your clutch when you go to a public restroom?

I usually use my clutch just for date nights when hubby can hold onto it. Recently, I had my clutch with me on a shopping excursion and panicked for a moment when I entered the restroom, but was thankful to remember that my clutch had a chain strap!

So, do you always make sure to buy a clutch with a strap for this purpose, keep it under your arm, or set it precariously on the toilet roll dispenser? What say you?