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 (14, 16, 18); 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 (14, 16, 18) to a next one of the plurality of line segments (14, 16, 18), 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 (14, 16, 18); 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 (14, 16, 18) to a next one of the plurality of line segments (14, 16, 18), 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.