Ternary I-III-VI nanocrystals, such as silver indium selenide (AISe), are candidates to replace cadmium- and lead-based chalcogenide nanocrystals as efficient emitters in the visible and near IR, but, due to challenges in controlling the reactivities of the group I and III cations during synthesis, full compositional and size-dependent behavior of I-III-VI nanocrystals is not yet explored. We report an amide-promoted synthesis of AISe nanocrystals that enables independent control over nanocrystal size and composition. By systematically varying reaction time, amide concentration, and Ag- and In-precursor concentrations, we develop a predictive model for the synthesis and show that AISe sizes can be tuned from 2.4 to 6.8 nm across a broad range of indium-rich compositions from AgIn11Se17 to AgInSe2. We perform structural and optical characterization for representative AISe compositions (Ag0.85In1.05Se2, Ag3In5Se9, AgIn3Se5, and AgIn11Se17) and relate the peaks in quantum yield to stoichiometries exhibiting defect ordering in the bulk. We optimize luminescence properties to achieve a record quantum yield of 73%. Finally, time-resolved photoluminescence measurements enable us to better understand the physics of donor-acceptor emission and the role of structure and composition in luminescence.