When the validity of a deductive conclusion conflicts with its believability people often respond in a belief-biased manner. This study used response times to test the selective processing model, which views belief-bias effects as arising from the interplay between superficial heuristic processes and more rigorous analytic processes. Participants were split into three response groups according to their propensity to endorse logically normative conclusions. The low-logic, high belief-bias group demonstrated rapid responding, consistent with heuristic processing. The medium-logic, moderate belief-bias group showed slower responding, consistent with enhanced analytic processing, albeit selectively biased by conclusion believability. The high-logic, low belief-bias group's relatively unbiased responses came at the cost of increased processing times, especially with invalid-believable conclusions. These findings support selective processing claims that distinct heuristic and analytic processing systems underpin reasoning, and indicate that certain individuals differentially engage one system more than the other. A minor amendment is proposed to the current selective processing model to capture the full range of observed effects.