Abstract Asymmetrically directed couplings in non-Hermitian systems cause directional amplification that leads to boundary skin state accumulation. However, counter-intuitively, the direction of accumulation may not follow that of the directed couplings. In this work, we demonstrate mechanisms where this accumulation can be systematically reversed without modifying the couplings at all, just by adjusting the system size or boundary conditions in a different, transverse direction.