A method of machining cooling holes includes providing a workpiece in which a cooling hole is to be formed. The cooling hole, once formed, defines distinct first and second sections. The workpiece is secured in a fixture that is mounted in a first machine. In the first machine, a laser is used to drill a through-hole in a wall of the workpiece. The through-hole is spatially common to the first and second sections of the cooling hole. After drilling the through-hole, the fixture with the workpiece secured therein is removed from the first machine and mounted in a second machine. In the second machine, 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.