How does a famous company prove dilution under the FTDA?

The Federal Trademark Dilution Act unambiguosly requires actual dilution, but not actual loss of sales or profits, but definitely more than likelihood of dilution or mere mental association, but not so much that direct evidence of dilution need be shown via consumer surveys --- although circumstantial evidence could be just right, especially if Victor's Little Secret was called Victoria's Secret.

"Use of the name 'Victor's Little Secret' neither confused any consumers or potential consumers, nor was likely to do so," Justice John Paul Stevens wrote for the court. The fact that a consumer may make the mental association between a famous trademark and a knockoff is not the same thing as showing that the famous name was damaged, Justice Stevens wrote. [WSJ]

Victoria's Secret...had argued that consumer surveys and other means of testing the public reaction to a trademark are expensive and can be difficult to arrange. Stevens noted that circumstantial evidence may be enough to show economic harm, particularly if the disputed business uses the same name as the well-known one. "Whatever difficulties of proof may be entailed, they are not an acceptable reason for dispensing with proof of an essential element," of the FTDA, Stevens wrote. [Associated Press]

Moseley d/b/a Victor's Little Secret v. V Secret Catalogue Inc., 01-1015

Also, Howard has some great background articles.