We derive a model-independent upper bound for the axial-vector form factor of the B→D* transition at zero recoil, FB→D*. The form factor turns out to be noticeably less than unity. The deviation FB→D* from unity is larger than previously anticipated. Using our estimate we extract Vcb from the measured exclusive rate of B→D*lν extrapolated to the point of zero recoil. The central "exclusive" value of Vcb is in agreement with the value obtained from the inclusive semileptonic width Γ(B→Xclν). We argue that the theoretical uncertainty in determining Vcb from the total inclusive width is significantly reduced if a constraint on the quark mass difference mb-mc stemming from the heavy quark expansion is taken into account.