The magnitudes of both void swelling and radiation-induced segregation (RIS) in austenitic iron-chromium-nickel alloys are dependent on bulk alloy composition. In this work, the resistance to swelling from major element segregation is estimated and alloys with greater nickel enrichment and fast-developing segregation profiles are shown to be less prone to swelling. In austenitic iron-chromium-nickel alloys, the total swelling depends on the duration of the transient swelling period that precedes steady-state swelling. A longer transient swelling period leads to less overall swelling for the same irradiation dose. The duration of this transient period depends on the void nucleation rate which is determined directly by the average vacancy diffusivity and indirectly by the magnitude of the segregation to the void surface. Alloys with faster vacancy diffusion have a slower void nucleation rate, a longer transient swelling period, and less swelling. Radiation-induced segregation affects swelling by decreasing the vacancy flux to the void. Because the diffusivity of nickel via the vacancy flux is slow relative to chromium, nickel enriches and chromium depletes at void surfaces during irradiation in all austenitic iron-chromium-nickel alloys. This local composition change reduces the subsequent vacancy flux to the voids, increasing the bulk point defect recombination rate, reducing the bulk vacancy concentration, which further reduces the nucleation rate and swelling. Alloys that display the greatest amount of nickel enrichment and chromium depletion are found to be most resistant to void swelling, as predicted from both void nucleation and void growth considerations.