Upconversion nanocrystals convert infrared radiation to visible luminescence, and are promising for applications in biodetection1-3, bioimaging4-7, solar cells8-10 and three-dimensional display technologies8,9,11. Although the design of suitable nanocrystals has improved the performance of upconversion nanocrystals10,12-14, their emission brightness is limited by the low doping concentration of activator ions needed to avoid the luminescence quenching that occurs at high concentrations15,16. Here, we demonstrate that high excitation irradiance can alleviate concentration quenching in upconversion luminescence when combined with higher activator concentration, which can be increased from 0.5 mol% to 8 mol% Tm31 in NaYF4. This leads to significantly enhanced luminescence signals, by up to a factor of 70. By using such bright nanocrystals, we demonstrate remote tracking of a single nanocrystal with a microstructured optical-fibre dip sensor. This represents a sensitivity improvement of three orders of magnitude over benchmark nanocrystals such as quantum dots17.