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After reviewing the simulation performance of general-to-specific automatic regression-model selection, as embodied in PcGets, we show how model selection can be non-distortionary: approximately unbiased ‘selection estimates’ are derived, with reported standard errors close to the sampling standard deviations of the estimated DGP parameters, and a near-unbiased goodness-of-fit measure. The handling of theory-based restrictions, non-stationarity and problems posed by collinear data are considered. Finally, we consider how PcGets can handle three ‘intractable’ problems: more variables than observations in regression analysis; perfectly collinear regressors; and modelling simultaneous equations without a priori restrictions.