The potent combination of DRM-free music, low cost, and the fact that what you buy plays on your iPod has made Amazon MP3 (see our review) the No. 3 online music store in just one month.

Hypebot, a music, technology, and new music business blog, reports that a number of record labels are saying privately that they believe Amazon MP3 has climbed past Rhapsody, Wal-Mart, and Napster to become the No. 3 retailer in downloaded sales of their music.

Amazon trails market leader iTunes and eMusic, although Hypebot speculates that Amazon MP3 could slip past eMusic to finish the year as the No. 2 online music retailer for some labels. The measurement here is dollars paid, not the number of tracks downloaded.

Napster, Napster, Napster. First you set the music world on fire (along with the legal system). Now you’re sort of an also-ran.

In yet another attempt to return to glory, Napster will rely less on its desktop client in favor of a Web-based approach as it hopes to attract more paying subscribers.

Napster seeks to make its platform more flexible and compatible with any Internet-enabled device with the release of Version 4.0. The move will allow Napster’s 770,000 subscribers to play their music from any computer without having to download additional software. Before today, Napster subscribers could only listen to their music after downloading the desktop client to their personal computers, although the Napster software is still required to transfer music from the service to compatible devices.

Napster sells music subscriptions for $10 to $15 a month, where customers can stream or download an unlimited number of songs from the company’s 5-million-song library.

“With this new platform Napster can easily be integrated into consumer electronics devices or integrated into other Web sites such as social networking sites,” said Christopher Allen, Napster’s chief operating officer.

Universal Music chief Doug Morris, considered by many to be the most powerful music executive in the universe, is launching an all-out assault on iTunes with a service to be called Total Music.

BusinessWeek reports that Morris is looking to join forces with other record companies to start an industry-owned all-you-can-eat subscription service tied to hardware such as MP3 players and cell phones. Sony BMG is already on-board, and Morris is also in talks with Warner Music Group. Together the three labels comprise about 75 percent of music sold in the United States.

Morris, whose company saw its earnings drop 25 percent in the first half of 2007, believes he and fellow music executives ceded too much control to Apple CEO Steve Jobs when the iTunes Music Store launched in 2003. As Morris said during a recent meeting, BusinessWeek notes, “We got rolled like a bunch of puppies.”