Originals: Yours Tonight by Martin Rev (covered by Cagney and Lacee)
The opening track on Cagney and Lacee's only album Six Feet of Chain is called "Be Mine" and is credited to Martin Rev. Now Mr Rev, of fab noisy electronic duo Suicide, did indeed release a track called Be Mine, it was on his album "See Me Ridin'" from 1996 - but the track "Be Mine" on Cagney and Lacee's 1997 album isn't a cover of that! No, Cagney and Lacee's "Be Mine" is actually a cover of "Yours Tonight" another track on "See Me Ridin'"
Again, not on YouTube so,
For Spotify users:
Not sure whether this was a mistake or intentional - I've decided it was a test for fans, one that I failed utterly completely by not discovering it until 15 years after Six Feet of Chain was released!
Update (14th July 2020): Currently on YouTube, so…
Audio: Cagney and Lacee - Be Mine