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Imputation of missing values is a strategy for handling non-responses in surveys or data loss in measurement processes, which may be more effective than ignoring them. When the variable represents a count, the literature dealing with this issue is scarce. Likewise, if problems of over- or under-dispersion are observed, generalisations of the Poisson distribution are recommended for carrying out imputation. In order to assess the performance of various regression models in the imputation of a discrete variable compared to classical counting models, this work presents a comprehensive simulation study considering a variety of scenarios and real data. To do so we compared the results of estimations using only complete data, and using imputations based on the Poisson, negative binomial, Hermite, and COMPoisson distributions, and the ZIP and ZINB models for excesses of zeros. The results of this work reveal that the COMPoisson distribution provides in general better results in any dispersion scenario, especially when the amount of missing information is large. When the variable presenting missing values is a count, the most widely used method is to assume that a classical Poisson model is the best alternative to impute the missing counts; however, in real-life research this assumption is not always correct, and it is common to find count variables exhibiting overdispersion or underdispersion, for which the Poisson model is no longer the best to use in imputation. In several of the scenarios considered the performance of the methods analysed differs, something which indicates that it is important to analyse dispersion and the possible presence of excess zeros before deciding on the imputation method to use. The COMPoisson model performs well as it is flexible regarding the handling of counts with characteristics of over- and under-dispersion, as well as with equidispersion.