The upper, equatorial, and lower diagnostics port plugs in ITER will include numerous intermingling labyrinths and many streaming paths whose impact should be carefully studied. For this purpose, the 3-D Discrete Ordinates code, Attila, has been routinely used by PPPL/UCLA to assess the nuclear field in these geometrically complex plugs both during operation and after shutdown. In this paper we describe the calculation procedure followed and the input parameters/assumptions applied to assess the shutdown dose rates (SDDR) everywhere with emphasize on their values inside the generic equatorial port plug (GEPP) and its inter-space extension area. Factors inherent in the Discrete Ordinates method that impact the accuracy of the results (e.g. quadrature sets used, boundary conditions applied, etc.) are discussed. Means to minimize streaming through straight gaps and open channels present in the GEPP are presented in this paper, along with an examination of their effectiveness in reducing the SDDR in the port inter-space area.