Do persistently low nominal interest rates mean that governments can safely borrow more? To addresses this question, I extend the model of Ghosh et al. [2013] to allow for persistent stochastic changes in nominal interest and growth rates. The key model parameter is the long-run difference between nominal interest and growth rates; if negative, maximum sustainable debts (debt limits) are unbounded. I show how both VAR- and spectral-based methods produce negative point estimates of this long-run differential, but cannot reject positive values at standard significance levels. I calibrate the model to the UK using positive but statistically plausible average interest-growth differentials. This produces debt limits which increase by only around 5% GDP as interest rates fall after 2008. In contrast, only a tiny change in the long-run average interest-growth differential - from the 95th to the 97.5th percentile of the distribution - is required to move average debt limits by the same amount.