Experimental data is presented which shows that laser scoring of glass sheets (112) with existing techniques produces unacceptable levels of residual stress in the separated sheets as the scoring speed is increased. Methods for solving this problem are disclosed which employ elongated and, preferably, asymmetrically-truncated laser beams (13). The methods allow glass sheets (112) to be scored at speeds of 1000 mm/s and above with low levels of residual stress, e.g., levels of residual stress which are less than or equal to 500 psi. Such low levels of residual stress translate into low levels of distortion during the manufacture of display panels (e.g., LCD panels) as well as in improved properties of the separated edges. The methods can be used with glasses of various types including glasses having low coefficients of thermal expansion.