Abstract: Ytterbium-doped LiYF4 (Yb:YLF) is a commonly used material for laser applications, as a photon upconversion medium, and for optical refrigeration. As nanocrystals (NCs), the material is also of interest for biological and physical applications. Unfortunately, as with most phosphors, with the reduction in size comes a large reduction of the photoluminescence quantum yield (PLQY), which is typically associated with an increase in surface-related PL quenching. Here, we report the synthesis of bipyramidal Yb:YLF NCs with a short axis of similar to 60 nm. We systematically study and remove all sources of PL quenching in these NCs. By chemically removing all traces of water from the reaction mixture, we obtain NCs that exhibit a near-unity PLQY for an Yb3+ concentration below 20%. At higher Yb3+ concentrations, efficient concentration quenching occurs. The surface PL quenching is mitigated by growing an undoped YLF shell around the NC core, resulting in near-unity PLQY values even for fully Yb3+-based LiYbF4 cores. This unambiguously shows that the only remaining quenching sites in core-only Yb:YLF NCs reside on the surface and that concentration quenching is due to energy transfer to the surface. Monte Carlo simulations can reproduce the concentration dependence of the PLQY. Surprisingly, Fo''rster resonance energy transfer does not give satisfactory agreement with the experimental data, whereas nearest-neighbor energy transfer does. This work demonstrates that Yb3+-based nanophosphors can be synthesized with a quality close to that of bulk single crystals. The high Yb3+ concentration in the LiYbF4/LiYF4 core/shell nanocrystals increases the weak Yb3+ absorption, making these materials highly promising for fundamental studies and increasing their effectiveness in bioapplications and optical refrigeration.