Bradford Hill's considerations published in 1965 had an enormous influence on attempts to separate causal from non-causal explanations of observed associations. These considerations were often applied as a checklist of criteria, although they were by no means intended to be used in this way by Hill himself. Hill, however, avoided defining explicitly what he meant by "causal effect". This paper provides a fresh point of view on Hill's considerations from the perspective of counterfactual causality. I argue that counterfactual arguments strongly contribute to the question of when to apply the Hill considerations. Some of the considerations, however, involve many counterfactuals in a broader causal system, and their heuristic value decreases as the complexity of a system increases; the danger of misapplying them can be high. The impacts of these insights for study design and data analysis are discussed. The key analysis tool to assess the applicability of Hill's considerations is multiple bias modelling (Bayesian methods and Monte Carlo sensitivity analysis); these methods should be used much more frequently.