Roll them up
I carry, in separate clean dry-cleaner plastic bags, one down-filled clean small pillow and one cashmere throw.
They roll up tight, small and very compact. They fit into the carryon that goes under the seat in front. I carry them no matter which class I am flying. They work for me. I know they are clean and comfortable. I will sleep well. You always need an extra pillow--and if the cabin is chilly, you need an extra wrap/blanket/throw.