Thick-shell CdSe/nCdS (n >10) nanocrystals were recently reported that show remarkably suppressed fluorescence intermittency or "blinking" at the single-particle level as well as slow rates of Auger decay. Unfortunately, whereas CdSe/nCdS nanocrystal synthesis is well-developed up to n < 6 CdS monolayers (MLs), reproducible syntheses for n > 10 MLs are less understood. Known procedures sometimes result in homogeneous CdS nucleation instead of heterogeneous, epitaxial CdS nucleation on CdSe, leading to broad and multimodal particle size distributions. Critically, obtained core/shell sizes are often below those desired. This article describes synthetic conditions specific to thick-shell growth (n> 10 and n> 20 MLs) on both small (sub2 nm) and large (>4.5 nm) CdSe cores. We find added secondary amine and low concentration of CdSe cores and molecular precursors give desired core/shell sizes. Amine-induced, partial etching of CdSe cores results in apparent shell-thicknesses slightly beyond those desired, especially for very-thick shells (n >20 MLs). Thermal ripening and fast precursor injection lead to undesired homogeneous CdS nucleation and incomplete shell growth. Core/shells derived from small CdSe (1.9 nm) have longer PL lifetimes and more pronounced blinking at single-particle level compared with those derived from large CdSe (4.7 nm). We expect our new synthetic approach will lead to a larger throughput of these materials, increasing their availability for fundamental studies and applications.