Several frameworks for group communication with ordering semantics such as causal and total ordering have been studied that provide different guarantees on the sequence in which messages are delivered at different sites. To accommodate application semantics, frameworks have also been proposed to weaken these semantics using application-specific information. We find that in many cases, an application may require messages to be delivered in a sequence satisfying certain constraints which requires strengthening rather than weakening of the ordering semantics. To accommodate this, we explore a new semantics, application order, that allows an application to specify an ordering specification order-spec. The multicast layer performs the necessary synchronization to ensure that the messages are delivered in an order satisfying order-spec. This semantics can be used in conjunction with existing ordering semantics, and eliminates many forms of application-level synchronization. It also expands the applicability of group communication frameworks by allowing communication primitives to be used directly in applications without additional synchronization.