We got our NIEs same day in Sevilla. We took the completed application forms, our passports with photocopies and our Copia Simple and photocopies. Once we reached the head of the queue the official checked the documents and made out two payment forms for us to take to the bank around the corner. Once they were receipted we took them back to the office, were called to the head of the queue, our receipts were checked and we were given our NIEs which are just A4 sheets. As I recall you need to give a reason for requiring an NIE. Ours, of course, was that we own a house here. I've heard that a rental agreement or an employers letter will be accepted too.