Register your Luxembourg domain name in Luxembourg
Luxembourg, officially the Grand Duchy of Luxembourg, is after Malta the smallest country of the European Union. Although it's a small country, it's one of the founders of several organisations such as the European Union, the Benelux, the NATO and the United Nations. The economy of Luxembourg evolved through the years into an economy that relies mainly on international trade and banking. The country has a thriving economy and is widely known. So definitely put a name under the .lu extension on your list of domain names.
Some good news? Currently there are no more restrictions to register a .lu domain name. Previously you needed to have a local contact in Luxembourg to be able to register a .lu name. However the restriction of the required local presence was lifted in February 2010 by Restena (.lu-registry).