Need ideas for stiff & very thin backing for my prints...

I float my images well inside an 8 ply matted frame, leaving typically a 1/4 inch or more space around, thus showing the matching backing paper placed behind the matt and print. I hinge my images from the top of the print and let gravity do its imperfect work. On most of my prints it doesn't bother me much that the paper waivers or stands free of the backing. But now I'm starting to use metallic paper for some very energetic images and I would prefer that the print be absolutely flat, but still be hinged from the top. Any suggestions for materials that won't add too much thickness to the print, but will stiffen them flat?

Thanks!

how about aluminum? it is very light weight and super thin. Might actually work well with a Metallic print

just a thought.

I thought about that, but everything I've seen using aluminum makes the print pretty thick.

I was thinking there was perhaps an adhesive I could use between the print and a piece of archival paper that in itself would supply the stiffness I'm looking for.

Aluminum sheet is your best bet but will need at least 1/32" I would think depending on the size of the print