Holes and clumps in the interstellar gas of dwarf irregular galaxies are gravitational scattering centres that heat field stars and change their radial and vertical distributions. Because the gas structures are extended and each stellar scattering is relatively weak, the stellar orbits remain nearly circular and the net effect accumulates slowly over time. We calculate the radial profile of scattered stars with an idealized model and find that it approaches an equilibrium shape that is exponential, similar to the observed shapes of galaxy discs. Our models treat only scattering and have no bars or spiral arms, so the results apply mostly to dwarf irregular galaxies where there are no other obvious scattering processes. Stellar scattering by gaseous perturbations slows down when the stellar population gets thicker than the gas layer. An accreting galaxy with a growing thin gas layer can form multiple stellar exponential profiles from the inside-out, preserving the remnants of each Gyr interval in a sequence of ever-lengthening and thinning stellar subdiscs.