Geological evidence indicates that the flow of the last European ice sheet was dominated by numerous large ice streams. Although some were ephemeral, most were sustained along well-defined axes at least during the period of retreat after the Last Glacial Maximum. A thermomechanically coupled three-dimensional numerical ice-sheet model has been used to simulate the ice sheet through the whole of the last glacial cycle, but with a spatial resolution that is high enough to capture streaming behaviour. An experiment with a smoothed bed is used to explore the self-organizing behaviour of streams when they are not forced by bed topography. On such a bed, streams typically have a width of 1–10 km, much narrower than the inferred European ice streams. An experiment using a realistic topography suggests that widths of ice streams are strongly influenced by topography, and tend to be of order 100 km. Moreover, even where the topography is muted, it stabilizes the locations of ice streams which, once formed, tend to be sustained along pre-existing axes. The model creates patterns of streaming that are similar to inferred patterns, suggesting strong topographic forcing. In a simulation using a realistic bed in which the ice was very cold and basal melting rarely occurred, streams were again very narrow. Widespread streaming under low driving stresses tends to reduce ice-sheet thicknesses compared with weak streaming or models that do not produce streaming. Consequently, ice thicknesses are smaller and tend to be consistent with the results of sea-level inversions based on geophysical Earth models.