This paper investigates the possibilities for structural optimisation of laser-welded sandwich panels with an adhesively bonded core and uni-directional vertical webs. Closed form expressions for the equivalent stiffness and elastic buckling strength of laser-welded sandwich panels are discussed and numerically evaluated to demonstrate the effect of parameter variations on stress and deflection. Due to the number of design variables and constraints a structural optimisation method based on the method of moving asymptotes (MMA) is implemented and used to minimise the structural weight per square meter of panel for a typical accommodation deck configuration. It is concluded that, within the span of production parameters and rule requirements, substantial improvements can be made with or without an adhesively bonded core. Without core material and without any changes to the surrounding structure the structural weight for standard production panels can be reduced considerably, by reducing the face plate thickness and by using thinner and fewer webs. Additional weight can be saved by removing all but a few webs and injecting low-cost polyurethane foam into the cavities, giving added thermal-acoustic insulation, or by incorporating a more structural core with greater thickness and higher density, by which the free span of the sandwich panel can be increased.