Limiting conditions for soot-particle inception were observed in microgravity spherical diffusion flames burning ethylene at 0.98 bar. Nitrogen was supplied to the ethylene and/or oxygen to obtain the broadest available range of stoichiometric mixture fraction, Zst. Both normal flames (surrounded by oxidizer) and inverse flames (surrounded by fuel) were considered. Soot-free conditions were found to be favored at increased Zst and there was no observed effect of convection direction on the sooting limits. The sooting limits follow a linear relationship between adiabatic flame temperature and Zst, with Zst accounting for a variation of about 700 K in the sooting-limit adiabatic flame temperature. This relationship is in qualitative agreement with a simple theory that assumes soot inception requires the local C/O atom ratio and temperature to be above threshold values, (C/O)c and Tc, respectively. The theory indicates that different mechanisms are responsible for sooting limits at low and high Zst. When inert is added to a fuel/air flame, a sooting limit is obtained when temperature becomes so low that the kinetics of soot inception are too slow to produce soot. On the other hand, a flame with a high Zst has low C/O ratios far into the fuel side of the flame. For such a flame, soot-free conditions can be attained at much higher temperatures because there is sufficient oxygen on the fuel side to favor oxidation of light hydrocarbons over formation of soot precursors.