We consider dynamic group services, where outputs based on small samples of privacy-sensitive user inputs are repetitively computed. The leakage of user input data is analysed, caused by producing multiple outputs, resulting from inputs of frequently changing sets of users. A cryptographic technique, known as random user selection, is investigated. We show the effect of random user selection, given different types of output functions, thereby disproving earlier work. A new security measure is introduced, which provably improves the privacy-preserving effect of random user selection, irrespective of the output function. We show how this new security measure can be implemented in existing cryptographic protocols. To investigate the effectiveness of our security measure, we conducted a couple of statistical simulations with large user populations, which show that it forms a key ingredient, at least for the output function addition. Without it, an adversary is able to determine a user input, with increasing accuracy when more outputs become available. When the security measure is implemented, an adversary remains oblivious of user inputs, even when thousands of outputs are collected. Therefore, our new security measure assures that random user selection is an effective way of protecting the privacy of dynamic group services.