In this paper, we address the medium-access control (MAC) problem in systems with multiple destinations, a problem that is crucial to the development of ad hoc networks. We focus on collision-resolution algorithms, specifically on First-Come, First-Serve (FCFS) splitting algorithms. We illustrate the difficulties that arise because of the interference between two populations of nodes that share a common channel, the most serious consequence of which is the possibility of deadlock that occurs when a well-known improvement for the single-destination case is used. Experimental results verify that the straightforward use of the FCFS algorithm in two-destination environments (without using this improvement) leads to deadlock-free performance. We show how performance can be improved by applying a time-division mechanism to separate interfering groups of nodes.