This paper explores the properties of pre-test strategies in estimating a linear Cliff-Ord-type spatial model when the researcher is unsure about the nature of the spatial dependence. More specifically, the paper explores the finite sample properties of the pre-test estimators introduced in Florax et al. (2003), which are based on Lagrange Multiplier (LM) tests, within the context of a Monte Carlo study. The performance of those estimators is compared with that of the maximum likelihood (ML) estimator of the encompassing model. We find that, even in a very simple setting, the bias of the estimates generated by pre-testing strategies can be very large and the empirical size of tests can differ substantially from the nominal size. This is in contrast to the ML estimator. However, if the true data generating process corresponds to the spatial error or lag model the issues arising with the pre-test estimators seem to be lessened.