A method for fabricating a part by selective melting or sintering of powder beds by high energy beam, the method including a) providing a material in the form of powder particles; b) depositing a first powder layer on a support; c) scanning a region of the first layer with the beam to heat the powder locally to a temperature higher than the powder sintering temperature, such that the powder particles as melted or sintered form a first single-piece element; d) depositing a second powder layer on the first powder layer; e) scanning a region of the second layer with the beam to heat the powder to a temperature higher than the powder sintering temperature, so that the particles of powder as sintered or melted form a second single-piece element; and f) repeating d) and e) for each new powder layer laid over a preceding layer until the part is formed.