http://www.copyright.iupui.edu/permfaq.htm#cov
How to record a cover song: “you issue the copyright owner a notice of intention to obtain a compulsory mechanical licence” then pay them 8¢, or 1.55¢ per minute (whichever is greater) per copy. (You don’t need the copyright owner’s permission.)
(I suppose this also means that 10¢ is about the least you’re ever going to pay for a track from an on-line music retailer.)