This paper introduces the Selective Traveling Salesman Problem with Draught Limits, an extension of Traveling Salesman Problem with Draught Limits, wherein the goal is to design maximal profit tour respecting draught limit constraints of the visited ports. We propose a mixed integer linear programming formulation for this problem. The proposed mixed integer program is used to solve –to optimality– small size instances and also to asses the quality of heuristic solutions found in the paper. The heuristic solutions are 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.