A method of laser trepan drilling diffuser type holes in a workpiece having an internal cavity, the said method comprising the steps of: laser drilling a hole of substantially constant cross-section through a wall of the workpiece; directing the beam of the laser such that the beam follows a path on at least one side of the hole to drill a diffuser section on at least the beam entry side of the hole with the beam exiting the hole substantially without interference with the remaining non-diffuser part of the hole, characterised in that the diffuser section is cut with a generally elongate opening on the beam entry side of the hole, with the beam being inclined with respect to the longitudinal axis of the hole, and with respect to the elongate axis of the said opening being formed on the beam entry side of the wall such that the beam is directed substantially wholly into the interior of the hole as it passes therethrough, the non-diffuser part of the hole comprising a substantially circular cross-section and the diffuser a substantially ovoid cross-section having a pair of semi-circular arcs joined together at their respective ends by a pair of straight parallel sides coincident with opposite sides of the said circular cross-section; wherein the beam is inclined with respect to the elongate axis of the opening by an angle of rotation determined by the steps of: determining the ratio of the length of the periphery of the said opening and half the length dimension of the opening in the direction of the major axis of the ovoid cross-section; determining a first angle with respect to a minor axis of the said ovoid cross-section by dividing 360 degrees by the said ratio to establish a first position on the periphery of the said circular cross-section, and the step of generating a line between the said first position with a second position on the ovoid at the transition from straight line to circular arc in the quadrant of the arc to be drilled, and determining the angle of rotation as the angle of the generated line with respect to the major axis of the ovoid. laser drilling a hole of substantially constant cross-section through a wall of the workpiece; directing the beam of the laser such that the beam follows a path on at least one side of the hole to drill a diffuser section on at least the beam entry side of the hole with the beam exiting the hole substantially without interference with the remaining non-diffuser part of the hole, characterised in that the diffuser section is cut with a generally elongate opening on the beam entry side of the hole, with the beam being inclined with respect to the longitudinal axis of the hole, and with respect to the elongate axis of the said opening being formed on the beam entry side of the wall such that the beam is directed substantially wholly into the interior of the hole as it passes therethrough, the non-diffuser part of the hole comprising a substantially circular cross-section and the diffuser a substantially ovoid cross-section having a pair of semi-circular arcs joined together at their respective ends by a pair of straight parallel sides coincident with opposite sides of the said circular cross-section; wherein the beam is inclined with respect to the elongate axis of the opening by an angle of rotation determined by the steps of: determining the ratio of the length of the periphery of the said opening and half the length dimension of the opening in the direction of the major axis of the ovoid cross-section; determining a first angle with respect to a minor axis of the said ovoid cross-section by dividing 360 degrees by the said ratio to establish a first position on the periphery of the said circular cross-section, and the step of generating a line between the said first position with a second position on the ovoid at the transition from straight line to circular arc in the quadrant of the arc to be drilled, and determining the angle of rotation as the angle of the generated line with respect to the major axis of the ovoid.