Intervened Poisson distribution (IPD) has been found suitable for dealing intervention problems of medical situations where positive Poisson distribution fails. Through this paper, we consider a class of discrete distributions suitable for situations of more than one intervention and a competitor to the truncated IPD. We attempt to study several properties of this class of distributions and a real life data set is considered to illustrate its application compared to truncated intervened Poisson distribution and truncated positive Poisson distribution.[PUBLICATION ABSTRACT]