A method, comprising: supporting a source glass sheet of 0.2 mm or less in thickness; defining a cutting line having at least one non-straight portion of a radius of less than 20 mm, where the cutting line defines a desired shape of a glass substrate; dividing the non-straight portion of the cutting line into a plurality of sequential line segments ; initiating a flaw in the glass sheet ; applying a laser beam to the glass sheet starting at the flaw and continuously moving the laser beam and the glass sheet relative to one another along the cutting line to elevate a temperature of the glass sheet at the cutting line; applying a cooling fluid simultaneously with the application of the laser beam to the glass sheet , such that the cooling fluid at least reduces the temperature of the glass sheet in order to propagate a fracture in the glass sheet along the cutting line; 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; further comprising varying the power level of the laser beam such that the power level is higher, by one of: at least 2%, at least 5%, and at least 10%, when the cutting line is straight as compared with when the cutting line is curved; and/or further comprising varying the speed of the movement of the laser beam relative to the glass sheet such that the speed is higher, by one of: at least 2%, at least 5%, and at least 10%, when the cutting line is straight as compared with when the cutting line is curved; and separating waste glass from the glass sheet to obtain the glass substrate of the desired shape. supporting a source glass sheet of 0.2 mm or less in thickness; defining a cutting line having at least one non-straight portion of a radius of less than 20 mm, where the cutting line defines a desired shape of a glass substrate; dividing the non-straight portion of the cutting line into a plurality of sequential line segments ; initiating a flaw in the glass sheet ; applying a laser beam to the glass sheet starting at the flaw and continuously moving the laser beam and the glass sheet relative to one another along the cutting line to elevate a temperature of the glass sheet at the cutting line; applying a cooling fluid simultaneously with the application of the laser beam to the glass sheet , such that the cooling fluid at least reduces the temperature of the glass sheet in order to propagate a fracture in the glass sheet along the cutting line; 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; further comprising varying the power level of the laser beam such that the power level is higher, by one of: at least 2%, at least 5%, and at least 10%, when the cutting line is straight as compared with when the cutting line is curved; and/or further comprising varying the speed of the movement of the laser beam relative to the glass sheet such that the speed is higher, by one of: at least 2%, at least 5%, and at least 10%, when the cutting line is straight as compared with when the cutting line is curved; and separating waste glass from the glass sheet to obtain the glass substrate of the desired shape. <EOS>