Sheet metal cutting using lasers is ubiquitous in the industry, and is used to produce everything from home decorations to excavator scoops. Metal waste is costly for the industry, both in terms of money, but also in terms of an increased environmental footprint. Tomologic develops a unique optimisation system that can reduce this waste drastically. This paper presents a CP approach to the Laser Cutting Path Planning Problem (LCPPP), a very hard important sub problem within the Tomologic optimisation system. A solution to the LCPPP is, given a packing of some details on a metal sheet, an ordering of the cuts necessary to separate the details from the sheet. The problem is complicated by physical factors such as heat from the laser beam, or details moving or flexing. In the paper, we explain the problem in detail and present our CP approach that we developed for solving the problem. The possibility (in CP) of custom search heuristics turned out to be crucial to be able to solve the problem efficiently, as these could be made to guide the search to good first solutions.