This talk is about estimation of multinomial parameters, from both Bayesian and non-Bayesian points of view, and presents an interesting link between the two. Jeffreys (1939) derived the uniform prior as the default prior for the Bayesian approach, by considering a multivariate hypergeometric model first. More recently, different 'reference' and 'overall objective' priors have been proposed. I argue that, especially in the presence of zero counts, these priors are too informative, and that there is no need to deviate from the uniform prior. Things are different when relatively many zero counts are present, however, and I will describe a generalisation of an existing approach to the binomial case of successes or failures only, allowing for (practically) zero parameters. This method seems to handle very well an extreme example provided by Prof. Jim Berger, when discussing the above candidate priors.