The finding that passeriform birds introduced to the islands of Hawaii and Saint Helena were more likely to successfully invade when fewer other introduced species were present has been interpreted as strong support for the hypothesis that interspecific competition influences invasion success. I tested whether invasions were more likely to succeed when fewer species were present using the records of passeriform birds introduced to four acclimatization districts in New Zealand. I also tested whether introduction effort, measured as the number of introductions and the total number of birds released, could predict invasion outcomes, a result previously established for all birds introduced to New Zealand. I found patterns consistent with both competition and introduction effort as explanations for invasion success. However, data supporting the two explanations were confounded such that the greater success of invaders arriving when fewer other species were present could have been due to a causal relationship between invasion success and introduction effort. Hence, without data on introduction effort, previous studies may have overestimated the degree to which the number of potential competitors could independently explain invasion outcomes and may therefore have overstated the importance of competition in structuring introduced avian assemblages. Furthermore, I suggest that a second pattern in avian invasion success previously attributed to competition, the morphological overdispersion of successful invaders, could also arise as an artifact of variation in introduction effort.