Numerous datasets contain excess zeroes, thus limiting their ability to be described via a standard distributional model. Accordingly, zero-inflated representations of these distributions have been developed to better describe such a random variable containing excess zeroes. In particular, the zero-inflated Poisson (ZIP) regression (Lambert, 1992; Hall, 2000) is a popular model to describe the relationship between a count response variable and explanatory variables of interest. The ZIP model has been used in a variety of applications, including manufacturing (Lambert, 1992), horticulture (Hall, 2000), zoology (Zipkin et al., 2014), and criminology (Famoye and Singh, 2006). Meanwhile, to address added over-dispersion that may exist in the data (even with accounting for the excess zeroes), the zero-inflated negative binomial (ZINB) model is often selected to address the matter, of which the zero-inflated geometric (ZIG) distribution (as discussed in Pandya et al., 2012, for example) is a special case. The ZIG regression is likewise considered as an alternative model in various applications such as those noted above. These and other zero-inflated models are available for use in the Vector Generalized Linear and Additive Models (VGAM) package (Yee, 2014) available for use in R (R Core Team, 2014). Over-dispersion is a common issue of many datasets. Excess zeroes are often thought of as a cause of data over-dispersion, however excess zeroes do not assure the existence of data over-dispersion. In actuality, excess zeroes reduce the mean of a dataset, thus inflating the dispersion index (variance divided by the mean); however, a severely under-dispersed dataset can still be under-dispersed even with the inclusion of excess zeroes in the data. Through broader examples, Sellers and Shmueli (2013) (in fact) illustrate that datasets with perceived forms of dispersion can actually stem from probability mixtures with different dispersion levels, including cases of over- or under-dispersion. One should therefore consider a flexible distribution that cannot only account for excess zeroes, but also address potential over- or under-dispersion in the distribution mixture. The Conway–Maxwell–Poisson (COM–Poisson) distribution of Conway and Maxwell (1962) is a flexible, two-parameter distribution for count data expressing over- or under-dispersion. Thus, a zero-inflated COM–Poisson (ZICMP) regression model would address the excess zeroes and provide flexibility in modeling data dispersion in a dataset. This work derives the ZICMP model and illustrates its flexibility and statistical properties. To first further motivate its use, Section 2 provides more details about the COM–Poisson distribution. Section 3 develops the ZICMP regression model. Section 4 illustrates the flexibility of this model to capture data dispersion associated with various simulated zero-inflated structures. Section 5 further demonstrates its adaptability through real and simulated examples. Finally, Section 6 concludes the manuscript with discussion.