Ramsey's theorem states that for any graph H there exists an n such that any 2-colouring of the complete graph on n vertices contains a monochromatic copy of H. Moreover, for large n, one can guarantee that there are at least c_H n^v copies of H, where v is the number of vertices in H. In this talk, we investigate the problem of optimising the constant c_H, focusing in particular on the case of complete graphs.