Methods and systems for drilling precise orifices in a wall of non-uniform thickness are provided. In one aspect, a thickness profile of at least a portion of the wall is created and the wall is irradiated with at least one laser beam to ablate a portion of the wall to thereby form an orifice in the wall. During the irradiation, one or more parameters of the least one laser beam are adjusted one or more times in accordance with the thickness profile to compensate for the non-uniform thickness of the wall.