[en] The neutron time-of-flight spectrometer NEAT at BER II is currently undergoing a major upgrade where an important aspect is the prevention of parasitic scattering to enhance the signal-to-noise ratio. Here, we discuss the impact of shielding to suppress parasitic scattering from two identified sources of background: the sample environment and detector tubes. By means of Monte Carlo simulations and a modification of the analytical model of Copley et al. [Copley and Cook, 1994], the visibility functions of instrument parts are computed for different shielding configurations. According to three selection criteria, namely suppression of background, transmission and detection limit, the parameters of an oscillating radial collimator are optimized for NEAT's default setup. Moreover, different configurations of detector shielding are discussed to prevent cross-talk within the radial detector system.