Does Buddhism Reject the concept of a Self / Soul Entirely or Just Its Permanence?

I'm a bit confused about the Buddhist doctrine of anatta (non-self). Does this teaching mean that Buddhism denies the existence of any kind of soul or self altogether? Or is it more accurate to say that Buddhism accepts some concept of a self, but denies that it is eternal, unchanging, or independent? I'd appreciate any clarification on whether the rejection is total or just about the soul's permanence.