We propose and investigate through Monte Carlo simulations two methods for Bayesian inference for the shape and the scale parameters of a Weibull distribution in a small and highly censored sample setting. The first method, WLB-SIR, is the Sampling Importance Resampling-adjusted Weighted Likelihood Bootstrap of Newton and Raftery. The second one is a new Bayesian Restoration Maximization BRM new algorithm working along the same line but replacing the bootstrap weighting step by a stochastic simulation step of the censored failure times. The advantage of the BRM method is that it takes account of the prior distribution in its first step. As a consequence, the Sampling Importance Resampling-adjusted version of BRM, BRM-SIR, is less fragile than WLB-SIR as it appears from our numerical experiments for Weibull parameters estimation. This article also includes a flexible procedure to transform prior knowledge into prior distributions on the Weibull parameters.