The present invention relates to laser-machining equipment (2) for etching grooves (8, 9) in a wall of a mechanical part (4), in particular of a crankshaft for an internal combustion engine, said equipment being provided with a fiber-optic laser device (12) and arranged to supply laser pulses. The fiber-optic laser device is controlled so that the laser pulses have a peak power that is greater than 400W and at least twice as great as the maximum average power of the laser device and so that the period of the laser pulses is in the nanosecond range (1 ns to 1000 ns) or lower. According to a first embodiment, the fiber-optic laser device is controlled in a QCW (quasi continuous wave) mode. According to a second, preferred, embodiment, the fiber-optic laser device is controlled in a triggered or Q-switched mode. The operating modes selected enable an increase in the effectiveness of the machining and to obtain a groove having an optimum cross-section, in particular a small mean radius of curvature at the bottom of the groove enabling accurate subsequent fracturing of the mechanical part using the least force.