We did a cover version of a song of another band. (With permission)

Are we allowed to put the acapella of our cover under a creative commons license or would we need an OK from the owners of the original song?

I am not really sure, but believe it would depend on the license of the original song. If the song is already licensed under a creative commons license, I believe you can cover the song as long as you comply with license requirements regarding attribution and commercial/non-commercial use. Certainly, folks at ccMixter cover each other’s CC-licensed songs on a regular basis. However, if the song is an “all rights reserved” song, I believe you need to have written permission of the copyright holder to cover the song, and to negotiate with the copyright holder the terms of licensing your cover. I do not believe you can license your cover with a CC license without permission from the copyright holder. This is a good question — perhaps someone knows more about this particular issue and can comment further. I imagine the Creative Commons organization would have more information regarding this issue.