(Bloomberg) -- The federal judge overseeing the Federal Trade Commission’s case to block Tapestry Inc.’s $8.5 billion takeover of rival Capri Holdings Ltd. rejected a bid by the companies to force antitrust enforcers to turn over more information about their definition of “accessible luxury” handbags.

In a ruling at a hearing Monday, Judge Jennifer L. Rochon in Manhattan said the FTC’s complaint offered enough detail on the proposed market in which Tapestry and Capri compete, with nine pages outlining the market. The companies filed a motion to force the FTC to offer more detail on the proposed market, arguing the complaint was too vague.

The judge said that if the companies disagree with her finding, they can deny the allegations and explore them further in discovery.

“The FTC laid out numerous parameters of the alleged relevant market,” she said. “At this point, notice is all that is required.”

The FTC sued to block the deal last month. Tapestry owns Coach, Kate Spade and Stuart Weitzman; Capri controls labels Michael Kors, Versace and Jimmy Choo. Rochon has scheduled a hearing in September to decide whether to put the merger on hold while the FTC pursues a case in its in-house court.

Rochon urged the companies and the FTC to discuss the market further, and said Tapestry can seek additional information from the agency directly in discovery, such as whether handbags are limited to women or also encompass bags used by men.

“There can be a conversation about what the appropriate parameters are,” she said.

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