The paper discusses the so-called exponential splitting method when the basic random variable has semi-heavy-tailed or heavy-tailed distribution. This method admits to represent the corresponding random variable as a mixture containing an exponential variable (phase) weighed by a ‘splitting probability’ p. The main purpose of the research is a searching for the values of parameters to maximize the probability p and hence to increase the frequency of the exponential phase. It allows to explore the memoryless property of the exponential distribution to construct, for example, regenerations in the corresponding queueing models. In particular, we focus on the optimal values of the parameters of Gamma and Pareto distributions.