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Aim: Reducing the rate of alien species introductions is a major conservation aim. However, accurately quantifying the rate at which species are introduced into new regions remains a challenge due to the confounding effect of observation efforts on discovery records. Despite the recognition of this issue, most analyses are still based on raw discovery records, leading to biased inferences. In this study, we evaluate different models for estimating introduction rates, including new models that use auxiliary data on observation effort, and identify their strengths and weaknesses. Innovation: We compare four models: (1) a naïve model which assumes perfect detection; (2) a model proposed by Solow and Costello (the S&C model); (3) constant detection model: a modified version of the S&C model with constant detection probabilities and (4) a novel sampling proxy model: a model that uses external data on observation effort. We simulate discovery records of varying lengths, introduction rates and temporal patterns of detection probabilities to explore scenarios under which these models accurately estimate underlying introduction rates. (5) We also include code to perform a model based on Belmaker using independent data on the number of native species. Main conclusion: We found that the length of the discovery records and the annual number of recorded species play a crucial role in the performance of all models. Under simulated scenarios of high detection, the naïve model is usually the best‐performing model, but it falls short when detection is low. Moreover, we find that in simulations which most likely mimic most real‐world cases (i.e. non‐monotonic probability of detection), incorporating external data on observation effort using the sampling proxy model, substantially improve estimates. This highlights the importance of considering observation effort when estimating introduction rates of alien species. To facilitate the use of these models, we provide a decision workflow and a dedicated R package ('alien'). [ABSTRACT FROM AUTHOR]