A method is described of radiatively cutting a wafer, the method comprising the steps of low power cutting of two trenches followed by high power cutting of a fissure. A single pulsed radiation beam is split into a first pulsed radiation beam for cutting at least one of the trenches and a second pulsed radiation beam for cutting the fissure. When cutting a fissure on the wafer in a cutting direction along a cutting street, the first and second radiation beams are directed simultaneously with the first radiation beam leading and the second radiation beam trailing. For cutting a fissure in the opposite cutting direction, a third pulsed radiation beam for trenching is split from said single pulsed radiation beam.