A method of machining cooling holes (64) includes providing a workpiece (60) in which a cooling hole is to be formed. The cooling hole, once formed, defines distinct first and second sections. The workpiece (60) is secured in a fixture (82) that is mounted in a first machine (84). In the first machine (84), a laser is used to drill a through-hole in a wall of the workpiece (60). The through-hole is spatially common to the first and second sections of the cooling hole. After drilling the through-hole, the fixture (82) with the workpiece (60) secured therein is removed from the first machine (84) and mounted in a second machine (86). In the second machine (86), ultrasonic machining is used to expand a portion of the through-hole to form the second section. An abrasive slurry used in the process is drained through the through-hole during the ultrasonic machining.