Łukasiewicz and, more recently, other philosophers have cast doubts on arguments from one version of determinism to another: roughly, from the view that every event (condition, state) has a cause or is determined, to the view that the remotest possible past determines the present and future. This paper defends a special class of such arguments. It identifies constraints on the relation of determination under which the arguments concerned are valid. And, by reference to the overall causal or determinational structure of the universe, it argues that the constraints themselves are highly plausible.