An H20 cooled compact MITR-II core, reflected by D20 has been designed for the MITR to increase the reflector thermal neutron flux at tips of beam ports by a factor of 3 or better, without changing the operating power level of the reactor. The diffusion approximation to the neutron transport equation has been used. A three neutron energy group scheme, that retains essential spatial effects, used in the studies has yielded satisfactory agreement with measured data. The factors which affect the intensity as well as the quality of the reflector thermal neutron flux have been studied. These studies show that the permanent features of the MITR limit the maximum power densities in the MITR-II core to factors between 4.5 and 12 below the corresponding values in reactors employing a similar core concept Nevertheless, the predicted unperturbed reflector thermal neutron flux of 1.lXlO14 n/cm 2-sec in MITR-II yields a reflector flux per unit power that is competitive with the corresponding values available in reactors of its type and a factor of 5.0 higher than that in MITR-I.