Lyric discussion by silburyhill 

"The Velvets" refer to characters in Neil Gaiman's tv series/novel Neverwhere...

@silburyhill Thank you for this hint. I researched a little more: The Velvets are beautiful and seductive vampires who need the warmth of others to survive. The catch is that the victim has to give him/herself voluntarily. So this fits perfectly into the thesis that the song is about past lovers as hinted by the quote on top of this discussion.

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