Standard spot return/forward premium regressions have long been known to provide a strong rejection of unbiasedness. However, due to the strong autocorrelation in the forward premium, which shows estimated autoregressive roots close and in some cases statistically indistinguishable from one, recent literature has cast doubt on the finite sample accuracy of these tests. In fact, finite sample size distortion has now come to be considered as one of several possible explanations behind the forward premium puzzle. In order to pursue this possibility further, we revisit the unbiasedness hypothesis using more appropriate inference procedures. In particular, rather than relying on standard stationarity-based asymptotics, we model the forward premium as a near-unit root process and then test unbiasedness using the bounds tests of Cavanagh et al. (1995) [Cavanagh, C.L., Elliott, G., Stock, J.H., 1995. Inference in models with nearly integrated regressors. Econometric Theory 11, 1131-1147.], which are explicitly designed to provide accurate size under near-unit root assumptions. To summarize our empirical findings, confidence intervals on the largest root confirm uncertainty regarding the stationarity/nonstationarity of the forward premium. However, estimates of the error correlation suggest only modest simultaneity bias. Consequently, we can still reject unbiasedness at the 5% level, even when using appropriately sized bounds tests. This evidence tends to suggest that the forward premium puzzle is more robust than previously imagined. It would be interesting in further work to explore to what extent such conclusions extend to alternative characterizations of the persistence in the forward premium, such as long-memory and structural break models.