Methods and apparatus provide for: cutting a thin glass sheet along a curved cutting line, where the curve is divided into a plurality of line segments; applying a laser beam and continuously moving the laser beam along the cutting line; applying a cooling fluid simultaneously with the application of the laser beam in order to propagate a fracture in the glass sheet along the cutting line; and varying one or more cutting parameters as the laser beam moves from one of the plurality of line segments to a next one of the plurality of line segments, wherein the one or more cutting parameters include at least one of: (i) a power of the laser beam, (ii) a speed of the movement, (iii) a pressure of the cooling fluid, and (iv) a flow rate of the cooling fluid.