Criteria for identifying optimal adjustment sets yielding consistent estimation with minimal asymptotic variance of average treatment effects in parametric and nonparametric models have recently been established. In a single treatment time point setting, it has been shown that the optimal adjustment set can be identified based on a causal directed acyclic graph alone. In a time-dependent treatment setting, previous work has established graphical rules to compare the asymptotic variance of estimators based on nested time-dependent adjustment sets. However, these rules do not always permit the identification of an optimal time-dependent adjustment set based on a causal graph alone. We extend those results by exploiting conditional independencies that can be read from the graph and demonstrate theoretically and empirically that our results can yield estimators with lower asymptotic variance than those allowed by previous results. We further show how our results allow for the identification of optimal adjustment sets based on a directed acyclic graph alone in the time-dependent treatment setting.