Estimates of the reliability of population viability analysis (PVA), accounting for uncertainties in model parameters, often arrive at confidence intervals for extinction probability so wide as to be almost meaningless. This lack of precision is a consequence of extreme sensitivity to average linear growth rate, when predicting to a distant time horizon. Longer-term trends or drift in parameter values (a form of ‘reddened’ environmental variability) will also affect the accuracy of such forecasts. This letter reports how, contrary to intuition, introducing such a component of variability may improve the precision of extinction forecasts. The paradoxical result arises because the dependence of extinction probability on growth rate is weakened, and shifted onto other parameters (e.g. diffusion strength) where dependence is less sensitive. This offers hope that, with reasonable knowledge of environmental stochasticity, it may still be meaningful to carry out longer range PVAs.