The standard 2-4-6 task requires discovery of a single rule and produces success rates of about 20%, whereas the dual-goal (DG) version requests discovery of two complementary rules and elevates success to over 60%. The experiment examined two explanations of DG superiority: Evans' (1989) positivity-bias account, and Wharton, Cheng, and Wickens' (1993) goal-complementarity theory. Two DG conditions were employed that varied the linguistic labelling of rules (either positively labelled Dax vs. Med, or mixed-valence "fits" vs. "does not fit"). Solution-success results supported the goal-complementarity theory since facilitation arose in both DG conditions relative to single-goal tasks, irrespective of the linguistic labelling of hypotheses. DG instructions also altered quantitative and qualitative aspects of hypothesis-testing behaviour, and analyses revealed the novel result that the production of at least a single descending triple mediates between DG instructions and task success. We propose that the identification of an appropriate contrast class that delimits the scope of complementary rules may be facilitated through the generation of a descending instance. Overall, our findings can best be accommodated by Oaksford and Chater's (1994) iterative counterfactual model of hypotheses testing, which can readily subsume key elements of the goal-complementarity theory. A subset of the data reported here formed part of a poster presented at the Twenty-Fourth Annual Conference of the Cognitive Science Society, Fairfax, Virginia, USA, August 2002.