Structural nested failure time models (SNFTMs) are models for the effect of a time-dependent exposure on a survival outcome. They have been introduced along with so-called G-estimation methods to provide valid adjustment for time-dependent confounding induced by time-varying variables. Adjustment for informative censoring in SNFTMs is possible via inverse probability of censoring weighting (IPCW). In the presence of considerable dropout, this can imply substantial information loss and consequently imprecise effect estimates. In this article, we aim to increase the efficiency of IPCW G-estimators under a SNFTM by deriving an augmented estimator that uses both censored and uncensored observations, and offers robustness against misspecification of the model for the censoring process, provided that a model for a specific functional of the survival time and time-dependent covariates is correctly specified. The empirical properties of the proposed estimators are studied in a simulation experiment, and the estimators are used in the analysis of surveillance data from the field of hospital epidemiology.