Based on Mitchell and Silver’s (1990) tower-building paradigm, the authors performed two experiments on multilevel quantity goals, strategies, and performance in task-interdependent groups. The study compared four goal types: IG (individual goal), GG (group goal), IG + GG (individual + group goal), and NSG (nonspecific goal). IG yielded low cooperation and performance, whereas, unexpectedly, NSG yielded high cooperation and performance. To explain this finding, we discerned two goal-setting components: Goal referent (performance-level targeted; individual/group) and goal specificity. Mediation analyses suggest that referent triggers a cooperation/competition mechanism, explaining the lower IG performance, whereas specificity triggers a speed/ accuracy mechanism, explaining the higher NSG performance. We conclude that individual goals can interfere with cooperative processes and group performance, and, for time-constrained interdependent tasks requiring speed and accuracy, specific difficult quantity goals may promote risk taking, thereby obstructing goal attainment.