Martin, There is indeed not much information out there -- poking around in the guts of the package I can't find much discussion, even in the draft chapters of the book Doug Bates is writing. I believe that "locally uniform" here has a technical meaning -- rather than meaning it is necessary exactly uniform; for example, the Jeffreys prior is (apparently) locally uniform. I am still trying to teach myself more about this -- my (old) copy of Bayesian Data Analysis isn't helping very much. (possibly? by Michael Höhle) The best I can do for myself at the moment is to poke through the code in lmer.c: within mer_MCMCsamp, the standard deviation is being sampled from an inverse-chi-squared distribution, scaled by the penalized weighted RSS; within MCMC_beta_u, the beta and u (random effect) values are sampled from normal distributions; within MCMC_S, the theta_S (random effect variances etc.) are also resampled from a normal distribution (probably on the log scale??) Sorry I can't be more helpful. Ben Bolker