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I like the Phyllis Hyman/ Norman Connors cover version. She was the real deal.Stylistic's "Betcha By Golly wow"
Perhaps avenged sevenfold is up your alley? They are a slight bit faster, but have some nice guitarwork and not too screamy. I'd also recommend sentenced/poisonblack (same singer, different band, about the same style) but that too is a bit faster most of the time.I listen to a bit of Black Sabbath, Nirvana, pearl Jam, Soundgarden and Alice in Chains once in a while.
My favourite albums are Metallica's first 4 though. Could anyone recommend me a band that sounds similar (fast, but not too fast, less screaming etc.)?