Additively manufactured Inconel 625 is particularly susceptible to the formation of niobium-rich δ-phase precipitates in the interdendritic regions during high temperature exposure. With specific minor alloying element combinations and nitrogen mass fractions on the order of 0.1 %, the formation of δ-phase can be suppressed through the precipitation of nitrides. For example, mass fractions of 0.39 % silicon and 0.03 % titanium led to the precipitation of Z-phase and η-nitrides, which consumed the excess niobium in the interdendritic regions and limited δ-phase formation. Even when holding the material at a temperature of 870 °C for 1000 h, the δ-phase volume fraction was approximately 2 %, which is far below the 6 % level observed in the wrought condition. When the titanium mass fraction was increased to 0.21 % and the silicon mass fraction decreased to 0.05 %, titanium-rich MN nitrides formed within the interdendritic regions instead. Since much of the Nb in these regions was not consumed by the nitrides, δ-phase formation was promoted and reached volume fractions above 10 %. The addition of a hot isostatic pressing step prior to high temperature exposure in both alloys produced a more uniform niobium distribution and minimized δ-phase formation at shorter times. At extended times, trends in the δ-phase volume fractions were similar to those observed in the as-deposited condition, with the initial alloy compositions driving differences in the distribution of excess niobium available for δ-phase formation.