A method for manufacturing material voxel-by-voxel using directed-energy deposition is given. Using the method, unsupported structures, via voxel-wise directed-energy deposition, with steep overhangs is described and demonstrated. Methods for forming arbitrarily-complex structures and shaped voxels and surfaces are also given. A method for forming materials with internally-varying properties is also given. The method utilizes a pulsed or modulated, rather than continuous-wave energy source, thus allowing rapid solidification of voxels, rather than contours, hatches or tracks. Tuning of pulsing or modulation, material flow, and deposition-path parameters allows the buildup of unsupported material using standard directed-energy deposition processing heads and 3-axis stages, for example. The methods are demonstrated using a modified-directed-energy-deposition processes and is applicable to powder-bed for the buildup of three-dimensional components, repair and the addition of features to existing components.