What is it called... (fascinator/hairband related)

[Trills]

What is it called when a fascinator or other head decoration is not on an alice band or a comb or a clip but on a flexible loop that goes all the way around your head?

(proper word needed for internet searching)

Headdress?

I think that's just another word for a fascinatory thing, it doesn't specify how it's attached.

Ah. Just thinking that 1920s flapper style accessories tend to be called headdresses, and they go right round the head. :)

Fair point :)