  We use a wide range of observations to constrain cosmological models
possessing a significant asymmetry in the lepton sector, which offer perhaps
the best chance of reconciling a critical-density Universe with current
observations. The simplest case, with massless neutrinos, fails to fit many
experimental data and does not lead to an acceptable model. If the neutrinos
have mass of order one electron-volt (which is favoured by some neutrino
observations), then models can be implemented which prove a good fit to
microwave anisotropies and large-scale structure data. However, taking into
account the latest microwave anisotropy results, especially those from
Boomerang, we show that the model can no longer accommodate the observed baryon
fraction in clusters. Together with the observed acceleration of the present
Universe, this puts considerable pressure on such critical-density models.
