We continue the work that was initiated in  on a fast marching-like method for simulating two-phase incompressible immiscible flow of water and oil in a porous medium. The purpose ot the present paper is threefold: (1) To provide an alternative derivation of the fast-marching-like method which reveals a strong connection to modern streamline methods. (2) To investigate the capabilities of this method as a tool for simulating realistic two-phase flow scenarios. In particular, we discuss, and demonstrate via numerical examples, two problems in this respect. First, the fast-marching-like algorithm does not always compute the correct solution. Second, the upwind difference scheme on which the method is based is inaccurate for flows parallel to high-contrast layers in the permeability field. (3) To present possible improvements of the work in  in order to deal with some of the concerns raised herein.