  We study the cake-cutting problem when agents have single-peaked preferences
over the cake. We show that a recently proposed mechanism by Wang-Wu (2019) to
obtain envy-free allocations can yield large welfare losses. Using a
simplifying assumption, we characterize all Pareto optimal allocations, which
have a simple structure: are peak-preserving and non-wasteful. Finally, we
provide simple alternative mechanisms that Pareto dominate that of Wang-Wu, and
which achieve envy-freeness or Pareto optimality.
