Bringing new wheels home on a plane. Help me protect them?

Hey everyone,

One thing led to another and I ended up buying a new set of wheels while on vacation, now I need to fly home with them. I'd rather not pay the special/oversized luggage fee since I already have a free extra bag included with my ticket, and the box is within the allowed dimensions for standard checked luggage.

The wheels came in a pretty sturdy box with custom-cut cardboard inserts that hold them snugly, so the packaging is already decent. That said, I want to give my new babies the best protection possible before handing them over to baggage handlers.

My current ideas:

• Fill empty spaces in the box with packing material (bubble wrap, foam, etc.)
• Add extra cardboard layers inside for additional rigidity

Has anyone done this before? Any tips or things I should watch out for?