Colloidal semiconductor nanocrystals, with intense and sharp-line emission between red and near-infrared spectral regions, are of great interest for optoelectronic and bio-imaging applications. The growth of an inorganic passivation layer on nanocrystal surfaces is a common strategy to improve their chemical and optical stability and their photoluminescence quantum yield. In particular, cation exchange is a suitable approach for shell growth at the expense of the nanocrystal core size. Here, the cation exchange process is used to promote the formation of a CdS passivation layer on the surface of very small PbS nanocrystals (2.3 nm in diameter), blue shifting their optical spectra and yielding luminescent and stable nanostructures emitting in the range of 700-850 nm. Structural, morphological and compositional investigation confirms the nanocrystal size contraction after the cation-exchange process, while the PbS rock-salt crystalline phase is retained. Absorption and photoluminescence spectroscopy demonstrate the growth of a passivation layer with a decrease of the PbS core size, as inferred by the blue-shift of the excitonic peaks. The surface passivation strongly increases the photoluminescence intensity and the excited state lifetime. In addition, the nanocrystals reveal increased stability against oxidation over time. Thanks to their absorption and emission spectral range and the slow recombination dynamics, such highly luminescent nano-objects can find interesting applications in sensitized photovoltaic cells and light-emitting devices.