Considering the increasing size of available data, the need for statistical methods that control the finite sample bias, while remaining computationally tractable, is growing. This is mainly due to frequent high dimensional settings that bring many inferential procedures to incur significant loss in terms of statistical and computational performance. We propose a simulation based method, the Iterative Bootstrap, that can be used, very generally, to remove the finite sample bias of consistent and nearly consistent estimators, when the number of parameters is allowed to increase with the sample size. It can be applied to a wide class of models and we consider here, in particular, the logistic regression model with possibly also random effects. We also show that the Iterative Bootstrap converges exponentially fast, which makes it a realistic algorithm in high dimensions.