The major problem in modeling count data is over-dispersion, which occurs as a result of long tail, too many occurrences of zeros or none occurrence than would normally be expected by Poisson and binomial distributions. The zero-truncated distributions arise in those situations where there is no zero by nature of the data (structurally).The existing zero-truncated distributions are not flexible enough to capture peculiar characteristics such as long tail as well as over-dispersion at the same time. The aim of this research was to develop and implement a more generalized zero-truncated distribution that come from the mixture of distributions for non-zero count data to include most of the characteristics which existing ones do not have. The specific objectives were to: (i) examine the issues zero-truncated count data; (ii) investigate the effectiveness of selected binomial-based distributions for count data with various dispersions; (iii) develop zero-truncated Com-binomial distribution; (iv) identify some properties of the newly developed distribution and (v) demonstrate the use and assess the performance of the distribution against some existing ones using real life datasets.rnFollowing mixture distribution methodology, the Zero-Truncated Com-Binomial (ZTCB) was derived from the mixture of Conway-Maxwell-Poisson generalization distribution to the Binomial distribution. The first two moments via probability generating function were also derived. The Maximum Likelihood Estimation of the parameters were also obtained by direct maximization of the log-likelihood function using â€œoptimâ€ routine in R software.rnThe findings of the study were:rn(i) the challenge in modeling count data, with a long tail and the problem arising from zeros (truncated or excess) were resolved;rn(ii) the Com-Binomial (CB) distribution outperformed other mixture distributions in handling either under-dispersion or over-dispersion situation;rn(iii) the probability mass function (pmf) of ZTCB distribution was derived and the first two moments were derived via probability generating function;rn(iv) the ZTCB distribution peaks around the mean to have two tails to resemble the normal distribution or peaks around 1 or n to resemble exponential distribution for carefully chosen parameter v . It is the generalization of the Zero-Truncated Com-Poisson, Zero-Truncated Poisson and Zero-Truncated Binomial distributions; andrn(v) the ZTCB distribution is more flexible to handle all levels of dispersion than Zero-Truncated Multiplicative Binomial distribution.rnThe study concluded that the ZTCB distribution which is characterized by two parameters is more flexible than other distributions. . It is recommended that when modeling structurally zero-truncated data, ZTCB distribution be used to obtain a robust result. This study therefore provides useful alternative to the existing distributions.