Local geometrical perturbations of alluvial channels can generate a pattern of non-migrating bars and pools. This phenomenon is known as “overdeepening”, because the pools locally enhance the scour in river bends. Overdeepening occurs only downstream of a perturbation if the channel is in the subresonant and subcritically damped regime, which corresponds to channels with moderate width-to-depth ratios. Previous theoretical analyses and laboratory experiments show that overdeepening occurs also upstream of geometrical perturbations in the relatively wide channels of the superresonant regime (Zolezzi & Seminara, 2001; Zolezzi et al, 2005; Mosselman et al, 2006). We use a two-dimensional depth-averaged morphological model to explore the occurrence of upstream and downstream overdeepening numerically. The simulations reproduce the overall picture arising from previous theoretical and experimental findings. Non-migrating bars and pools appear downstream of perturbations if the regime is subresonant. The bar pattern appears both upstream and downstream if the regime is superresonant. However, two findings in the computational results differ from linear theory. First, the threshold between subresonant and superresonant regimes is higher in the numerical computations than predicted by linear theory. Second, at very high width-to-depth ratios in the superresonant regime, the computed non-migrating bars are shorter than predicted by linear theory (and observed experimentally). We explain the higher threshold from numerical diffusion, and the shorter bars from limited simulation duration, numerical diffusion and the non-linear effects suggested by Siviglia et al (2011).