Schematic image of a model of magma storage and transport under an Icelandic rift-zone volcanic system, adapted from [2,3]. The observations and interpretations used to develop this model are described in the main text. Storage, cooling and crystallization are trans-crustal. Magma storage is dominated by stacked sills which may have a vertical thickness of about 10 m. Some eruptions are fed directly and rapdily from near-Moho magma storage zones, and undergo minimal interaction with the crust in transit. Pervasive, trans-crustal mush is not a feature of this model. Transient, spatially restricted mush zones are, however, present around the open liquid of the thin sills. (Online version in colour.)