These headphones really suck. The sound quality is terrible, like a tin can. And the connection to the jack is so bad that there's background noise when you're trying to listen to your music. Also, the "cover" you mentioned is just some sort of cloth pouch with Velcro sewn on. There are many other headphones in the same price range, like the Panasonic RP-HJE120, that have a much clearer connection, good sound quality, and a variety of colors. I highly recommend them.
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