Current models are too noisy to predict climate usefully on decadal timescales, but two-stage post-processing of model outputs greatly improves predictions of decadal variations in North Atlantic winter climate. Quantifying signals and uncertainties in climate models is essential for the detection, attribution, prediction and projection of climate change(1-3). Although inter-model agreement is high for large-scale temperature signals, dynamical changes in atmospheric circulation are very uncertain(4). This leads to low confidence in regional projections, especially for precipitation, over the coming decades(5,6). The chaotic nature of the climate system(7-9)may also mean that signal uncertainties are largely irreducible. However, climate projections are difficult to verify until further observations become available. Here we assess retrospective climate model predictions of the past six decades and show that decadal variations in North Atlantic winter climate are highly predictable, despite a lack of agreement between individual model simulations and the poor predictive ability of raw model outputs. Crucially, current models underestimate the predictable signal (the predictable fraction of the total variability) of the North Atlantic Oscillation (the leading mode of variability in North Atlantic atmospheric circulation) by an order of magnitude. Consequently, compared to perfect models, 100 times as many ensemble members are needed in current models to extract this signal, and its effects on the climate are underestimated relative to other factors. To address these limitations, we implement a two-stage post-processing technique. We first adjust the variance of the ensemble-mean North Atlantic Oscillation forecast to match the observed variance of the predictable signal. We then select and use only the ensemble members with a North Atlantic Oscillation sufficiently close to the variance-adjusted ensemble-mean forecast North Atlantic Oscillation. This approach greatly improves decadal predictions of winter climate for Europe and eastern North America. Predictions of Atlantic multidecadal variability are also improved, suggesting that the North Atlantic Oscillation is not driven solely by Atlantic multidecadal variability. Our results highlight the need to understand why the signal-to-noise ratio is too small in current climate models(10), and the extent to which correcting this model error would reduce uncertainties in regional climate change projections on timescales beyond a decade.