Dual-process theories come in many forms. They draw on the distinction between associative, heuristic, tacit, intuitive, or implicit processes (System 1) and rule-based, analytic, explicit processes (System 2). We present the results of contextual manipulations that have a bearing on the supposed primacy of System 1 (Stanovich & West, 2000). Experiment 1 showed that people who evaluated logically valid or invalid conditional inferences under a timing constraint (N=56), showed a smaller effect of logical validity than did people who were not placed under a timing constraint (N= 44). Experiment 2 similarly showed that stressing the logical constraint that only inferences that follow necessarily are to be endorsed (N = 36) increased the size of the validity effect, as compared to that of participants (N=33) given the standard instruction to make "logical" inferences. These findings concur with the thesis in dual-processing frameworks that "Rationality-2 processes" (Evans & Over, 1996), "test procedures" (Chater & Oaksford, 1999), or "conclusion validation processes" (Johnson-Laird Byrne, 1991; Schroyens, Schaeken, & d'Ydewalle, 2001) serve to override the results of System 1 processes.