This paper explores, primarily by means of analysis, the differences that can exist between individual and aggregate loss guarantees in an environment where guarantees are only provided at an aggregate level. The focus is on understanding which traffic parameters are responsible for inducing possible deviations and to what extent. In addition, we seek to evaluate the level of additional resources, e.g., bandwidth or buffer, required to ensure that all individual loss measures remain below their desired target. The paper's contributions are in developing analytical models that enable the evaluation of individual loss probabilities in settings where only aggregate losses are controlled, and in identifying traffic parameters that play a dominant role in causing differences between individual and aggregate losses. The latter allows the construction of guidelines identifying what kind of traffic can be safely multiplexed into a common service class.