This paper is interested in the small sample properties of the indirect inference procedure which has been previously studied only from an asymptotic point of view. First, we highlight the fact that the Andrews (1993) median-bias correction procedure for the autoregressive parameter of an AR(1) process is closely related to indirect inference; we prove that the counterpart of the median-bias correction for indirect inference estimator is an exact bias correction in the sense of a generalized mean. Next, assuming that the auxiliary estimator admits an Edgeworth expansion, we prove that indirect inference operates automatically a second order bias correction. The latter is a well known property of the Bootstrap estimator; we therefore provide a precise comparison between these two simulation based estimators.