  Recent results have suggested that the density of baryons in the Universe,
OmegaB, is much more uncertain than previously thought, and may be
significantly higher. We demonstrate that a higher OmegaB increases the
viability of critical-density cold dark matter (CDM) models. High baryon
fraction offers the twin benefits of boosting the first peak in the microwave
anisotropy power spectrum and of suppressing short-scale power in the matter
power spectrum. These enable viable CDM models to have a larger Hubble constant
than otherwise possible. We carry out a general exploration of high OmegaB CDM
models, varying the Hubble constant h and the spectral index n. We confront a
variety of observational constraints and discuss specific predictions. Although
some observational evidence may favour baryon fractions as high as 20 per cent,
we find that values around 10 to 15 per cent provide a reasonable fit to a wide
range of data. We suggest that models with OmegaB in this range, with h about
0.5 and n about 0.8, are currently the best critical-density CDM models.
