 Bromberger’s flagpole counterexample provides a severe test of this requirement. The reason why the inference from the length of the shadow to the height of the flagpole is non-explanatory is because the length of the shadow is not nomically responsible for the flagpole’s height. Hempel’s original conditions could not cope with situations of this kind, where inferences using laws support predictions and retrodictions that are not also explanations, even though they satisfy all four. This alternative condition thus requires that the properties cited in the antecedent of the lawlike premise(s) must be nomically relevant to the explanandum or may not be included there (Fetzer 1981, 1992). The height of the flagpole, but not the length of the shadow, qualifies as nomically relevant, which resolves the quandary—at the expense of acknowledging classes of arguments that are predictive or retrodictive but not explanatory, even when they involve inferences from law(s) that satisfy Hempel’s original criteria. The reformulated conditions are: