Nonindigenous invasive plants pose a major threat to natural communities worldwide. Biological control of weeds via selected introduction of their natural enemies can affect control over large spatial areas but also risk nontarget effects. To maximize effectiveness while minimizing risk, weed biocontrol programs should introduce the minimum number of host-specific natural enemies necessary to control an invasive nonindigenous plant. We used elasticity analysis of a matrix model to help inform biocontrol agent selection for garlic mustard (Alliaria petiolata (M. Bieb.) Cavara and Grande). The Eurasian biennial A. petiolata is considered one of the most problematic invaders of temperate forests in North America. Four weevil species in the genus Ceutorhynchus (Coleoptera: Curculionidae) are currently considered potential biocontrol agents. These species attack rosettes (C. scrobicollis), stems (C. roberti, C. alliariae), and seeds (C. constrictus) of A. petiolata. Elasticity analyses using A. petiolata demographic parameters from North America indicated that changes in the rosette-to-flowering-plant transition and changes in fecundity consistently had the greatest impact on population growth rate. These results suggest that attack by the rosette-feeder C. scrobicollis, which reduces overwintering survival, and seed or stem feeders that reduce seed output should be particularly effective. Model outcomes differed greatly as A. petiolata demographic parameters were varied within ranges observed in North America, indicating that successful control of A. petiolata populations may occur under some, but not all, conditions. Using these a priori analyses we predict: (1) rosette mortality and reduction of seed output will be the most important factors determining A. petiolata demography; (2) the root-crown feeder C. scrobicollis will have the most significant impact on A. petiolata demography; (3) releases of single control agents are unlikely to control A. petiolata across its full range of demographic variability; (4) combinations of agents that simultaneously reduce rosette survival and seed production will be required to suppress the most vigorous A. petiolata populations. These predictions can be tested using established long-term monitoring sites coupled with a designed release program. If demographic models can successfully predict biocontrol agent impact on invasive plant populations, a continued dialogue and collaboration between empirical and theoretical approaches may be the key to the development of successful biocontrol tactics for plant invaders in the future.