We show how to implement a bounded time queue for two different processes. The time queue is a variant of a priority queue with elements from a discrete universe. The bounded time queue has elements from a discrete bounded universe. One process has time constraints and may only spend constant worst case time on each operation while the other process may spend more time. The time constrained process only has to be able to perform some of the time queue operations while the other process has to be able to perform all operations. We show how to do a deamortization of the deleteMin cost and to provide mutual exclusion for the parts of the data structure that both processes maintain.