A nozzle for an ink-jet printer is provided. The nozzle is manufactured from a heat-softenable tube and has a gradually converging inner diameter leading to an orifice less than 30 microns in diameter and an outer nozzle diameter proximate the orifice at least as great as the outer diameter at other points along the tube. The nozzle is produced by heating a short segment of a heat-softenable tube while rotating it, until said segment is sufficiently softened to cause the inner diameter to converge at an angle (α) between 6 and 26 degrees with respect to the axis of symmetry (74) of the tube, and until the inner diameter is equal to or less than a selected orifice diameter. The gradual taper is achieved solely as a result of heat-activated surface forces inherent in the tube material and without external drawing or pulling of the tube. Further the gradual taper facilitates achieving a desired orifice dimension during removal of a portion of the tube having an innner diameter less than the selected orifice diameter. The extremely small orifice size enables an ink-jet printer to deposit droplets of ink sufficiently small to make photographic-quality gray scale and color images. Such a nozzle can also advantageously be used for biological, medical and pharmaceutical apparatuses and devices.