This paper presents a globally converging decision-directed blind adaptive algorithm for carrier phase offset recovery of 8-VSB signals. We show that the decision-directed blind phase-recovery algorithm has a well-behaved cost function similar to the cost function of blind phase-recovery algorithms based on high-order statistics. Hence, simple decision-directed phase recovery can replace blind phase-recovery algorithms for 8-VSB, which have high jitter noise. We also devise an adaptive mechanism to ensure global convergence, i.e., to remove the undesirable local minima that occur in most blind algorithms. Therefore, the proposed algorithm achieves not only global convergence but also minimum mean squared error jitter noise performance.