Abstract The concept of a Z-number has a potential for many applications, especially in the realms of computation with probabilities and events described in natural language (NL). Of particular importance are applications in economics, decision analysis, risk assessment, prediction, anticipation, planning biomedicine and rule-based manipulation of imprecise functions and relations. The main critical problems that naturally arises in processing Z-information is informativeness of computation and reasoning with Z-information. An importance of informativeness issue for dealing with Z-numbers was first mentioned by Prof. L. Zadeh. Z-number is informative if its value has high specificity and same time arises a question what level of informativeness of a resulting Z-number sufficient for intelligent decision making. The existing literature devoted informativeness of computation with Z-numbers is quite scarce. All the existing works on computation of Z-numbers are characterized by increasing of entropy. In particular, these approaches are not able to account for informativeness of computation results. This study presents some results of investigations on informativeness of Z-number calculus by using concept of specificity and concept of horizontal membership functions. We propose a strategy for optimizing informativeness of Z-number operations with desired degree of specificity. Comparative analysis of different measures of specificity of Z-numbers is given. Validity of the proposed approach is illustrated in examples.