Last.fm, the London-based music site acquired by CBS last spring, announced earlier this week it had lined up all four major labels to offer free music on demand. The advertising-supported feature lets anyone listen to any track, for up to three plays.

Because three plays are probably not going to satisfy that itch to hear your favorite song every hour of every day, Last.fm also announced it would soon implement a subscription service offering unlimited plays. Other than saying it would happen, Last.fm has not offered any other details about the subscription service, but The New York Times said it would be a pay service.

Music from Last.fm’s on-demand service is streamed to listeners and cannot be saved to hard drives or moved to other devices, such as a personal MP3 player.

By itself, because of the three-song limit, Last.fm’s free on-demand service is hardly an alternative to owning your own music, or, for that matter, subscribing to one of the existing services such as Napster, which offers an all-you-can-download subscription for a flat monthly rate. Current music subscription models such as Napster use digital rights management technology that stops the music from playing once a subscriber cancels his subscription.

Even while the last of the Last.fm news stories slowly faded from the mid-week news cycle, another Web company was rumored to be negotiating a music download service all its own.

Yahoo is supposedly in early discussions to sell unprotected MP3s or offer them for free in an advertising-supported platform.

A Yahoo spokesperson said the company has wanted to offer DRM-free songs, and that the issue has been on the table during discussions with the labels. However, the representative denied that talks with the labels had stepped up in recent weeks, or that any decision is forthcoming in the near future.