Our goal here is to determine the spatial and temporal constraints on communication between two observers at least one of which moves with constant proper acceleration in two-dimensional Minkowski spacetime. We take as a simplified model of communication one observer bouncing a light signal off another observer. Our derivations use only elementary mathematics and spacetime diagrams, and hence are accessible to students taking their first course in special relativity. Furthermore, the qualitative features of our results can be easily explained to non-physics students in courses that discuss special relativity at a "conceptual" level. (Contains 8 figures.)