We determine the anomalous dimensions of baryon operators for the three color theory as function of the number of massless flavours within the conformal window to the maximum known order in perturbation theory. We show that the anomalous dimension of the baryon is controllably small, within the δ-expansion, for a wide range of number of flavours. We also find that this is always smaller than the anomalous dimension of the fermion mass operator. These findings challenge the partial compositeness paradigm.