The effect of the shape and dimensions of zinc oxide nanocrystals on the threshold and directionality of UV lasing in the nanocrystals has been investigated. The results indicate that hexagonal columnar nanocrystals have the lowest optical threshold pump power at nanoresonator diameters of 100-200 nm, comparable to the absorption path length of the excitation light. The laser radiation is shown to have a mode structure, being directed predominantly along the prism axis. The lasing mechanism in prismatic nanocrystals differs from that in hexagonal-pyramidal nanocrystals. Electron microscopy results show that the ZnO nanocrystals are highly uniform in shape and size and that these parameters depend on the chemical vapor deposition conditions.