This paper introduces the selective traveling salesman problem with draft limits, an extension of the traveling salesman problem with draft limits, wherein the goal is to design a maximum profit tour respecting draft limit constraints at the visited nodes. We propose a mixed integer linear programming (MILP) formulation for this problem. This MILP model is used to solve—to optimality—small size instances and to assess the quality of solutions obtained using a general variable neighborhood search heuristic that explores several neighborhood structures. Our extensive computational experiments confirm the efficiency of the method and the quality of the reported solutions.