An inverse dose-rate effect has sometimes been observed for mutagenesis in cells exposed to gamma-rays. We model such data quantitatively with the key assumption that the effect is caused in cycling cells by correlated variations in sensitivity across the cell cycle, for both mutation and killing. We quantify this approach using the LQR (linear-quadratic + resensitization) formalism, which describes the response to radiation of a heterogeneous cell population. This model is applied to an exponentially growing population. We compare its predictions with dose- and dose-rate dependent mutation data and show that it can well fit the observed inverse dose-rate effect, as well as providing an explanation of why inverse dose-rate effects have been seen in some experiments, but not in others. The actual values of the model parameters emerging from the analysis are reasonable in magnitude, based on their biological interpretations. We conclude that the LQR model can quantify cell-cycle redistribution effects without overparameterization, and that the data favour a correlation explanation of inverse dose-rate effects for mutagenesis by low-LET radiation. It is less clear that this explanation is appropriate to high-LET radiation-induced oncogenic transformation, although all potential explanations of inverse dose-rate effects predict that, at appropriately low doses, no dose-rate effects of any kind are expected.