If overdispersion occur as a result of excessive zero counts “i.e, zero inflation”, Zero Inflated Poisson/Negative Binomial distributions are preferred over the standard Negative Binomial distribution as they have a parameter that handles excessive zeros. Without doubting their outstanding performance in modeling overdispersed and zero inflated datasets, there are concerns as to whether zero inflated distributions should always substitute standard distributions in these types of datasets. For this reason, this paper intended to use different real datasets to show that zero inflated models are not always necessary even if the data is characterized by overdispersion and zero inflation. This was achieved through comparing Negative Binomial distribution with Zero Inflated Poisson/Negative Binomial distributions in datasets that went through the test of overdispersion and zero inflation. With respect to goodness of fit of these distributions, zero inflated distributions scored higher AIC scores in all datasets when compared to Negative Binomial distribution. Negative Binomial was marked as the outstanding distribution in all datasets suggesting that zero inflated models are not always necessary in datasets caharacterized by overdispersion and zero inflation.