Supraglacial deposits are known for their influence on glacier ablation. The magnitude of this influence depends on the thickness and the type of the deposited material. The effects of thin layers of atmospheric black carbon and of thick moraine debris have been intensively studied. Studies related to regional-scale deposits of volcanic tephra with thicknesses varying between millimetres and metres and thus over several orders of magnitude are scarce. We present results of a field experiment in which we investigated the influence of supraglacial deposits of tephra from Grímsvötn volcano on bare-ice ablation at Svínafelsjökull, Iceland. We observed that the effective thickness at which ablation is maximized ranges from 1.0 to 2.0 mm. At ~10 mm a critical thickness is reached where sub-tephra ablation equals bare-ice ablation. We calibrated two empirical ablation models and a semi-physics-based ablation model that all account for varying tephra-layer thicknesses. A comparison of the three models indicates that for tephra deposits in the lower-millimetre scale the temperature/radiation-index model performs best, but that a semi-physics-based approach could be expected to yield superior results for tephra deposits of the order of decimetres.