Toward a truly photostable PbSe quantum dot (QD), we apply the thick-shell or "giant" QD structural motif to this notoriously environmentally sensitive nanocrystal system. Namely, using a sequential application of two shell-growth techniques-partial-cation exchange and successive ionic layer adsorption and reaction (SILAR)-we are able to overcoat the PbSe QDs with sufficiently thick CdSe shells to impart new single-QD-level photostability, as evidenced by suppression of both photobleaching and blinking behavior. We further reveal that the crystal structure of the CdSe shell (cubic zinc-blende or hexagonal wurtzite) plays a key role in determining the photoluminescence properties of these giant QDs, with only cubic nanocrystals sufficiently bright and stable to be observed as single emitters. Moreover, we demonstrate that crystal structure and particle shape (cubic, spherical, or tetrapodal) and, thereby, emission properties can be synthetically tuned by either withholding or including the coordinating ligand, trioctylphosphine, in the SILAR component of the shell-growth process.