Recoaters are described which are adapted for use in powder-layer three-dimensional printers. The recoaters comprise a mesh discharge device that is adapted to be selectively activated by the application of an agitation, e.g. a vibration. Such mesh discharge devices include a planar mesh, i.e. a screen or sieve, which is adapted to support a quantity of powder when the quantity of powder and the mesh are static and to dispense at least a portion of the quantity of powder when at least one of the quantity of powder and the mesh is agitated. Preferably, the mesh is disposed substantially horizontally, but may be disposed at an angle to the horizontal. Also described are powder-layer three-dimensional printers comprising such recoaters. In some embodiments, the powder-layer three-dimensional printers are adapted to space the mesh no more than about two to ten powder layer thicknesses from the top surface of the powder bed or substrate upon which a powder layer is to be deposited.