It's unlikely to happen, but make sure whatever species you are importing does not end up on CITES list.

I had to send some avian blood (frozen, in gel packs) by courier to the US, and it was returned because some kind country had added their entire bird list - which included this species - a common cage bird in the UK - onto the Cites list, so blood products could only be exported with a CITES export certificate. Lacking this, US customs kindly (and unfortunately quite properly) sent it back

Trying to get a CITES export certificate for a species which is a common cage bird in the UK was yet more fun - I eventually had to offer to take pictures of the birds to show that they were not wild caught as they were yellow and white, and wild caught birds were green....