I understand that you will need both parts, not necessarily when you pick up the car, but definitely when you are driving on the road as if you were unfortunate to be involved in an incident and the police were present you have to be able to present your driving licence (both parts) together with the rental agreement / insurance on demand.

Should have added I believe that you also need your passport when driving too.

Can those in the know (Roger) confirm exactly what documents we need to have when driving in the US ?