3-D numerical models describing convection cells that may develop in a buoyant layer over an upper-mantle hotspot are developed. Results are compared with those of an alternative model, which assumes an upper partially molten layer having the same density as the underlying mantle, but of much higher viscosity. Geophysical and geochemical data over Iceland are used to assess the models. For the case of a buoyant upper layer, a major finding of our modelling is the prediction of a cold downward moving sheet in the upper layer situated just above the axis of the hot underlying mantle hotspot. When compared to geophysical data from Iceland, this modelled feature may explain why: (i) along the hotspot axis, seismic tomography reveals a mantle that remains cold down to ∼80 km depth; (ii) the ridge crest systematically avoids the axis of the hotspot and (iii) the ridge axis is displaced by ∼60 km to the east or the west of the hotspot axis, these ridge axes corresponding to the modelled upwellings of hot material in the uppermost layer driven by the cold downwelling axial sheet. Finally, the model also predicts development of gravity swells a few hundred kilometres long and several tens of kilometres wide, with a peak to valley amplitude of 5–10 mGal, lying over ascending sheets of upwelling material that float over the hotspot. Comparison with the residual gravity map over Iceland does indeed show the presence of a long gravity high along the active eastern section of the ridge. Over the AskjaVolcano, the long gravity high intersects an off-axis gravity high oriented northwest, which joins the Kolbeinsey Ridge. It is proposed that this branching may be the cause of the eastward drift of the western section of the Iceland ridge that took place 3 Ma. Further south, parallel to the same ridge-associated positive gravity anomaly, a more recent branching is found with a very long gravity high, oriented in an easterly direction, but that eventually contours the whole eastern coast of Iceland. This latter feature may be the precursor of future eastward drift of the whole eastern section of the ridge. When combined with experimentally derived models of dry peridotite melting, it is found that the temperature field of the models is consistent with the principal constraints derived from compositional characteristics of Icelandic basalts and the 3-D map of the upper mantle below the Icelandic hotspot derived from S-wave seismic tomography. The high viscosity layer model is also relatively successful at explaining geophysical and petrological data, except that it does not predict the development of hot and cold sheets in the partially molten mantle, and it leads to a large and strong negative gravity and bathymetry anomaly over the Iceland Hotspot, at a place where available data show a swell. However, this latter result is found to depend on the lateral boundary conditions used in the numerical modelling. For this reason we conclude that the presence of a very high viscosity layer below the ridge cannot be ruled out on the basis of gravity and bathymetric data alone. On the other hand, the influence of a floating upper layer provides an interesting and plausible alternative to explain available geophysical data, given that experimental data tend to indicate only modest changes in viscosity of the mantle in response to partial melting.