This paper is about two controversial inference-patterns involving counterfactual or subjunctive conditionals. Given a plausible assumption about the truth-conditions of counterfactuals, it is shown that one can't go wrong in applying hypothetical syllogism (i.e., transitivity) so long as the set of worlds relevant for the conclusion is a subset of the sets of worlds relevant for the premises. It is also shown that one can't go wrong in applying antecedent strengthening so long as the set of worlds relevant for the (...) conclusion is a subset of that for the premise. These results are then adapted to Lewis's theory of counterfactuals. (shrink)