We analyse those models of the Universe consistent with the observed isotropy, entropy, element abundances and with the existence of galaxies. The finiteness of the entropy per baryon in the Universe today, Sb ∼ 108, limits the amount of dissipation that could have taken place in the past and hence the degree of irregularity allowed in the singularity structure. This observation essentially rules out the chaotic cosmology in its full generality and appears to constrain the singularity to be of simultaneous Robertson–Walker character containing only small curvature fluctuations.