The conditions under which flux limitation of thermal conductivity begins to affect laser-induced compression by restricting the energy flow to the ablation zone are considered. On the assumption that the maximum thermal flux is given by Fm = α (1/4 ne ve ) kT, a simple analytic model is used to show that flux limiting commences when the ratio of the critical radius to the ablation radius rc/ra ⪆ (α/16)[(8 AM)/(πmZ)]½. The laser power at which this occurs varies as α3/λ2. Computer modelling is used to check the validity of these predictions.