The EU is considering changing the legal definition of absinthe. Turns out that currently, you call us the name even for a product with no thujone. (See the Erowid page for more on absinthe.)
Europe explores how to define the "green fairy" (Yahoo! News)
Thujone, whose latin name is Artemisia absinthium, is a toxin extracted from wormwood plants that some EU lawmakers worry is too harmful, especially in higher concentrations.
Under current EU regulations, absinthe does not have to contain any thujone to justify the name, but also must not exceed a maximum of 35 milligrams of thujone per kilogram.
In order to standardize the content, the European Commission has proposed that anything labeled "absinthe" must have at least 5 and maximum of 35 milligrams of thujone per kilogram.