A combination of premises such as "Person A asserts that if and only if he's a liar, then person B is a liar" and "Person B asserts that person A is a truth-teller", with the question what the status of persons A and B might be (truth-teller or liar), elicits meta-propositional reasoning, that is, reasoning about the truth and falsity of propositions. Both an inference rule and a mental models approach have been proposed to explain for meta-propositional reasoning. These proposals are compared to one another with respect to the strategies that people use, and this suggests that the proposed strategies are to a large extent ad hoc amendments to either theory. A review of a series of studies (Schroyens, 1995), controlling some confounding aspects in previous research, gives little evidence for a specific short-cut strategy that hinges on making backwards inferences. This counters the original proposal of Johnson-Laird and Byrne (1990) and recent corroborations of this strategy (Byrne & Handley, 1997; Schroyens, Schaeken, & d'Ydewalle, 1995). Other findings of our studies, however, indicate that, relative to the starting hypothesis by which one enters the formal structure of the problems, reasoners do not always engage in an exhaustive search strategy. This counters Rips (1989, 1990a) rule-based model, but is in accordance with the mental model theory's principle that a validating search for counter-examples is carried out by default but is not invariably complete.