Hat wearers of RoF

I have just bought a splendid hat to wear on my holibobs, BUTTTTTT I have no hat box type case, and I don't want to wear it.

It's also short hall to France.

Does anyone have any recommendations for hat cases that can also be used to transport bits and bobs for my carry-on?

 

I find my hats fit almost perfectly on my head.  They need very little maintenance other than occasional rearrangement to ensure the jauntiest of angles.  I have four baseball caps and three large floppy cricket hats.