We study the slot allocation problem where agents have quasi-linear single-peaked preferences over slots and identify the rules satisfying efficiency, strategy-proofness, and individual rationality. Since the quasi-linear single-peaked domain is not connected, the famous characterization of the Vickrey rule in terms of Holmström (1979)'s three properties cannot be applied. However, we are able to establish that on the quasi-linear single-peaked domain, the Vickrey rule is still the only rule satisfying efficiency, strategy-proofness, and individual rationality.