We revisit a paper of J. Steel ("Determinacy in the Mitchell Models" AML, 1980, 22, pp 109 - 125) to calculate afresh levels of determinacy available in core models in the region of strong cardinals. This involves a Friedman game for the Comparison Lemma, and one interpretation of the results is as an answer to the question "How much of the axioms of ZFC Set Theory is needed to prove the Comparison Lemma for these classes of models?