The classical canonical Ramsey theorem of Erdos and Rado states that, for a
ny integer q greater than or equal to 1, any edge colouring of a large enou
gh complete graph contains one of three canonically coloured complete subgr
aphs of order q. Of these canonical subgraphs, one is coloured monochromati
cally while each of the other two has its edge set coloured with many diffe
rent colours. The paper presents a condition on colourings that, roughly sp
eaking, requires them to make effective use of many colours ('essential inf
initeness'); this condition is then shown to imply that the colourings in q
uestion must contain large refinements of one of two 'unavoidable' colourin
gs that are rich in colours. As it turns out, one of these unavoidable colo
urings is one of the canonical colourings of Erdos and Rado, and the other
is a 'bipartite variant' of this colouring.