While we acknowledge the inadequacy of the standard treatment of fallacies (see Hamblin 1970, p. 12) when it comes to assessing the normative dimension of argumentation, we suggest that its definition of fallacious arguments sheds light on another issue of interest to argumentation scholars, namely rhetorical effectiveness. Specifically, we contend that this definition contains a fundamental intuition regarding the way fallacies are processed: if fallacies are misidentified as valid (or acceptable/reasonable/unproblematic) arguments, then it means that their fallaciousness remains undetected. This, in itself, justifies an inquiry into how they manage to remain undetected, which is what this chapter sets out to do by drawing on a cognitive pragmatic account of meaning. Chiefly, our task will be to explain how successful fallacies constrain evaluation so as to bypass or withstand critical testing. This involves the formulation of argumentative messages which strengthen the content of the fallacy to make it epistemically stronger and cognitively easy to process and/or weaken potential or actual refutations on the same two dimensions (epistemic strength and ease of processing). In a nutshell, our contribution (i) develops the rationale for envisaging rhetorical effectiveness in terms of foregrounding and backgrounding processes, (ii) explains how the linguistic choices made in fallacious arguments may decisively constrain cognitive processes and in particular evaluative processes, and (iii) illustrates these phenomena through a discussion of naturally-occurring examples of fallacious argumentation.