Separation vessels are traditionally designed based on rules of thumb that guide the designer to a feasible solution. Despite its widespread use, this approach presents important limitations, which is mostly that there are no concerns about the identification of an optimal solution. Recently, the use of mathematical programming was proposed to solve the design problem of a vertical separation vessel through a mixed-integer linear programming procedure. However, despite the advantages of the mixed-integer linear model, this method has important shortcomings. In this article, we show deficiencies of this linear model and we present a mixed-integer nonlinear model solved using a mixed-integer nonlinear programming procedure. We briefly highlight the importance of using discrete standard values of pipes as well as plates for the design. We also address the use of different recommendations associated to the height of the vessel, thus generating conservative as well as optimistic models and we extend the scope of the design problem to the inclusion of demisters.