A method of laser drilling a delivery port (37) in a beneficial agent dispenser (30) is disclosed. A dispenser (30) has a compartment (32) formed by a wall (31) for containing a beneficial agent (33) to be delivered. A laser beam is employed for burning at least partially through the wall (31). The laser beam and the dispenser (30) are positioned relative to one another such that the laser beam is aimed at a predetermined port site (35) on the dispenser (30). The laser beam is turned off (unenergized) during the positioning period. The laser beam is then energized and moved relative to the dispenser (30) for scribing a delivery port (37) proximate the port site (35). The scribing motion moves the laser beam from the port site (35) along a course (37). Preferably the course (37) is closed. The scribing motion causes the burning of the wall (31) by the laser beam to scribe the delivery port (37). The positioning motion and the scribing motion are controlled by a scanning system (16). The laser source (13) beam is energized during the scribing motion for burning the wall (31) forming the delivery port (37) therein for subsequent delivery of the beneficial agent (33) therethrough.