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Senior Judge James W. Haley Jr. stated in a separate opinion that agreed in part and dissented in part with the majority that Mr. Hadeed had not proved that the reviewers were not customers — he only suspected they were not.

“A business subject to critical commentary should not be permitted to force the disclosure of the identity of anonymous commentators simply by alleging that those commentators may not be customers because they cannot identify them in their database,” the judge said, adding that Mr. Hadeed’s complaints were likely a “self-serving argument.”

The Washington Post filed a friend of the court brief in support of Yelp, as did Gannett Co. Inc., the Reporters Committee for Freedom of the Press and the American Society of News Editors.

Mr. Levy said the case was the first he had seen in which the court ordered revelation of information on anonymous users.

“I’ve litigated in many cases for 14 years, and it’s the first time I’ve ever seen an appellate court order the identification, the first case in which I’ve represented a party in which we thought the Doe was clearly protected and the court said they were not,” he said.

Yelp allows users to post reviews on local businesses and services and is a popular place to complain or compliment restaurants and shops. Yelp users are estimated to have written more than 39 million reviews.

Hadeed Carpet, which advertises heavily throughout the D.C. area and in The Washington Times, has a two out of five star rating on Yelp, based on nine reviews. The ninth review was posted Wednesday and is a one-star condemnation of Hadeed’s lawsuits.

But the review site also has a long, contentious history of hiding reviews, listing them as “not recommended.” Hadeed Carpet has 88 hidden reviews, the majority of them negative, though the business has received a number of five-star reviews.

Mr. Hadeed has responded to most of the reviews his business has received, thanking the good reviews and saying he wants to address the concerns of negative reviewers. The response to negative reviews always asks for more information, including the Yelp user’s full name.

Mr. Delaney argued that the fact Mr. Hadeed had so many hidden reviews is telling. Reviews typically are hidden only when Yelp suspects them of being false or violating its terms of service.

“The problem we had was that these posts were not filtered; they were out there in the open. After we complained, Yelp filtered them,” he said. “What does that tell you?”

A second business, Hadeed Oriental Rug Cleaning, has fared little better among users, garnering 2.5 stars from seven reviews. The hidden reviews are roughly split between negative and positive.