Current trends in the embedded systems field tend to collocate multiple functionalities upon a single computing platform, the aim being to reduce both the size and cost of embedded systems. Nevertheless, it is unlikely that all functionalities share the same level of criticality, and certification of the system has to be achieved using varying degrees of rigorousness. Typically, a task tau_i is guaranteed to meet its temporal constraints up to a criticality level that is equal to its own criticality. When those conditions are no longer met, i.e. when another higher priority task tau_j has its execution time that exceeds its Worst Case Execution Time (WCET) w.r.t. the criticality level of tau_i, a common approach is to suspend tau_i. However, in some cases, it may not be necessary to suspend tasks with a lower criticality immediately as they could still be executed without compromising the deadlines of high criticality tasks. As a step towards this aim, we propose a method, denoted Latest Completion Time (LCT), that allows lower criticality tasks to proceed with their execution as long as they do not prevent higher criticality tasks from meeting their deadlines. Furthermore, we show that tasks suspension can only be temporary, and prove that a particular definition of idle times can be used to reset the system's criticality level. Finally, we study the performances of our LCT mechanism w.r.t. the classical mechanism that suspends a task as soon as the system criticality level becomes higher than its own criticality.