The new Ni-Fe-based superalloy DT706, derived from INCONEL 706, is the object of studies for potential uses in turbine-disk applications at temperatures above 973 K. This alloy aims at improving the microstructural stability while preserving the excellent machinability and good mechanical properties of the base material. This article is the first of a two-part study concentrating on the characterization of the microstructure of the DT706 precipitates, depending on the heat-treatment conditions. Analyses were performed by means of ex-situ small-angle neutron scattering (SANS) measurements, together with conventional scanning electron microscopy (SEM) and transmission electron microscopy (TEM) microscopy, on experimentally-heat-treated samples. The results, when compared to a similar analysis previously made on INCONEL 706, showed that the precipitation characteristics of DT706 reflect compositional changes, but are still remarkably dependent on the cooling stages between the different heat-treatment steps.