When analyzing the round complexity of multi-party computation MPC, one often overlooks the fact that underlying resources, such as a broadcast channel, can by themselves be expensive to implement. For example, it is impossible to implement a broadcast channel by a deterministic protocol in a sub-linear in the number of corrupted parties number of rounds. The seminal works of Rabin and Ben-Or from the early 80's demonstrated that limitations as the above can be overcome by allowing parties to terminate in different rounds, igniting the study of protocols with probabilistic termination. However, absent a rigorous simulation-based definition, the suggested protocols are proven secure in a property-based manner, guaranteeing limited composability. In this work, we define MPC with probabilistic termination in the UC framework. We further prove a special universal composition theorem for probabilistic-termination protocols, which allows to compile a protocol using deterministic-termination hybrids into a protocol that uses expected-constant-round protocols for emulating these hybrids, preserving the expected round complexity of the calling protocol. We showcase our definitions and compiler by providing the first composable protocols with simulation-based security proofs for the following primitives, relying on point-to-point channels: 1 expected-constant-round perfect Byzantine agreement, 2 expected-constant-round perfect parallel broadcast, and 3 perfectly secure MPC with round complexity independent of the number of parties.