  In this work, we introduce a new Asymptotic Norming Property (ANP) which lies
between the strongest and weakest of the existing ones, and obtain isometric
characterisations of it. The corresponding w*-ANP turns out to be equivalent on
the one hand, to Property $(V)$ introduced by Sullivan, and to a ball
separation property on the other. We also study stability properties of this
new ANP and its w*-version.
