Standard real-time models do not consider the fact that a chosen technical deadline is different from the critical latency where the service utility becomes zero. This is in mismatch with engineering practice. In this paper we propose a tolerance-based refinement of the real-time model. By doing so we make the process of deriving the estimation of the critical latency explicit. The difference between the technical deadline and the critical latency is a measure for the safety margin of the system. This safety margin is important for both, soft real-time and hard real-time systems, though with different quantities and qualities. Furthermore, we explain why the critical latency can hardly be quantified by a concrete value. However, we demonstrate how to derive reasonable estimates for it. We use a concrete application to show how the distinctive knowledge of the critical latency and the technical deadline are useful for real-time scheduling.