The type of absinthe that can be imported back from Mexico is subject to rules by the U.S. Food and Drug Administration (FDA) and the Department of the Treasury’s Alcohol and Tobacco Tax and Trade bureau regulations. The absinthe must be “thujone free” which means that it contains less than 100 parts per million of thujone. It is alleged that thujone caused the psychotropic effects of absinthe before the drink was regulated. The word ""absinthe cannot be the brand name, nor can it stand alone on the label. The artwork may not project images of psychotropic, mind-altering or hallucinogenic effects. Absinthe that violates any of these rules can be seized.
You may have to pay a small duty when you bring back more than one liter of alcohol. This alcohol must be for personal use only, and you must be 21 years of age to carry alcohol across the border. If you are carrying what the government refers to as an unusual amount, you may be suspected of not bringing the alcohol back for personal use. You should call ahead to the port you plan to enter through if you will be bringing back a substantial quantity of alcohol.
Different states that you may arrive in will have different laws about what you can bring with you. These are in addition to the federal laws listed above. Some states may require an alcohol-related license to carry more than a certain amount. Check with the alcohol beverage control board of the state you are traveling to in order to ensure that you comply with state laws and regulations.