Summary Parasitoids often are selected for use as biological control agents because of their high host specificity, yet such host specificity can result in strong interspecific competition. Few studies have examined whether and how various extrinsic factors (such as parasitism efficiency, i.e. the ability to optimize host‐finding attack rates) influence the outcome of competition between parasitoids, even though they could have profound effects on the implementation of classical biological control programmes. To determine the potential influence of extrinsic competition and coexistence on host suppression efficacy, we compared parasitism by two larval parasitoids (Tetrastichus planipennisi and Spathius galinae) of the invasive emerald ash borer (EAB) Agrilus planipennis, under different host densities, parasitoid densities, host plant sizes and parasitoid–host ratios. Spathius galinae had significantly higher parasitism efficiency (≈4 times), but significantly lower brood size (>6 times) than that of T. planipennisi. The attack rates of hosts increased significantly with parasitoid density, whereas host density did not significantly affect multiparasitism. The parasitism rate of T. planipennisi on small host logs was significantly higher than that on large logs, while host plant (log) size had no significant impact on S. galinae parasitism. The multiparasitism rate was rather low regardless of host log size and parasitoid/host density, indicating that intrinsic competition between the two species of parasitoids might seldom occur in the field. The two species of parasitoids could therefore coexist in the same habitat, and any adverse effects on the suppression of EAB populations caused by competitive behaviour between the two species of parasitoids would likely be negligible. Synthesis and applications. Our findings suggest that introducing multiple species of parasitic natural enemies could be feasible for management of invasive species, but it is important to examine multiple extrinsic factors simultaneously when evaluating interspecific competition between them. Among these different extrinsic factors, we found that coexistence between parasitoids can be mediated by trade‐offs in their parasitism efficiency and brood sizes. Thus, the differences in life‐history traits of natural enemies could be used to select among biological control agents being considered for releases.