A music company’s demand that YouTube take down a 29-second home video of two children dancing to a song by Prince backfired Monday when a federal appeals court used the case to make it harder for copyright-holders to act against brief, non-commercial uses of their material. Recording companies, motion picture studios and other copyright owners issue numerous takedown notices each day, targeting everything from home videos to campaign ads that include segments of songs or newscasts. When a copyright-holder tells a website like YouTube that one of its postings violates the holder’s exclusive rights to license the material, federal law requires that the posting be removed immediately. Fair use includes journalistic accounts and criticism, educational uses for teaching or research, and brief, private postings that don’t damage the commercial market for the work. Lenz, who lives in Pennsylvania, posted the homemade video of her children dancing and bouncing in the kitchen to Prince’s “Let’s Go Crazy,” playing on a home stereo, in February 2007. Universal had assigned a staffer to monitor YouTube for Prince’s songs and send takedown notices for any postings that made what the company considered “significant use” of the material — anything longer than a one-second excerpt of a song that isn’t drowned out by background noise. The staffer decided that “Let’s Go Crazy” was the focus of Lenz’s video, and Universal directed YouTube, owned by Google, to remove the posting. Universal did not pursue a claim of copyright infringement, but Lenz sued the company under a law allowing damages for mistaken or wrongful denial of access to a posting or publication.