A method for laser processing a transparent workpiece such as a glass substrate, the method comprising: providing a transparent workpiece, directing a laser beam onto the workpiece to thereby form a contour line in the transparent workpiece, along which contour line the transparent workpiece is separable, wherein the laser beam is a pulsed laser beam emitted by a laser beam source, wherein the pulsed laser beam is localized in the transparent workpiece, the pulsed laser beam propagating along a beam pathway in a z direction, which pulsed laser beam has: a wavelength λ; a non-axisymmetric beam cross section; a maximum beam intensity; an effective spot size w o,eff, which effective spot size is defined as a shortest radial distance in any direction from the beam propagation pathway z at which beam intensity decreases to 1/e 2 of the maximum beam intensity; a pulse energy and pulse duration sufficient to exceed a damage threshold of the transparent workpiece to thereby form the contour line in the transparent workpiece which contour line comprises a defect in the transparent work piece; characterized in that the non-axisymmetric beam cross section has a minimum Rayleigh range Z Rx,min in the x-direction and a minimum Rayleigh range Z Ry,min in the y-direction, wherein the smaller of the minimum Rayleigh range in both the x and y direction is the distance along the beam pathway at which the optical intensity of the beam decays to one half of the maximum beam intensity, and, wherein F D = the smaller of Z Rx, min and Z Ry, min / π W 2 o, eff / λ, wherein F D is a dimensionless divergence factor having a value of 10 or greater. providing a transparent workpiece, directing a laser beam onto the workpiece to thereby form a contour line in the transparent workpiece, along which contour line the transparent workpiece is separable, wherein the laser beam is a pulsed laser beam emitted by a laser beam source, wherein the pulsed laser beam is localized in the transparent workpiece, the pulsed laser beam propagating along a beam pathway in a z direction, which pulsed laser beam has: a wavelength λ; a non-axisymmetric beam cross section; a maximum beam intensity; an effective spot size w o,eff, which effective spot size is defined as a shortest radial distance in any direction from the beam propagation pathway z at which beam intensity decreases to 1/e 2 of the maximum beam intensity; a pulse energy and pulse duration sufficient to exceed a damage threshold of the transparent workpiece to thereby form the contour line in the transparent workpiece which contour line comprises a defect in the transparent work piece; characterized in that the non-axisymmetric beam cross section has a minimum Rayleigh range Z Rx,min in the x-direction and a minimum Rayleigh range Z Ry,min in the y-direction, wherein the smaller of the minimum Rayleigh range in both the x and y direction is the distance along the beam pathway at which the optical intensity of the beam decays to one half of the maximum beam intensity, and, wherein F D = the smaller of Z Rx, min and Z Ry, min / π W 2 o, eff / λ, wherein F D is a dimensionless divergence factor having a value of 10 or greater. a wavelength λ; a non-axisymmetric beam cross section; a maximum beam intensity; an effective spot size w o,eff, which effective spot size is defined as a shortest radial distance in any direction from the beam propagation pathway z at which beam intensity decreases to 1/e 2 of the maximum beam intensity; a pulse energy and pulse duration sufficient to exceed a damage threshold of the transparent workpiece to thereby form the contour line in the transparent workpiece which contour line comprises a defect in the transparent work piece; characterized in that the non-axisymmetric beam cross section has a minimum Rayleigh range Z Rx,min in the x-direction and a minimum Rayleigh range Z Ry,min in the y-direction, wherein the smaller of the minimum Rayleigh range in both the x and y direction is the distance along the beam pathway at which the optical intensity of the beam decays to one half of the maximum beam intensity, and, wherein F D = the smaller of Z Rx, min and Z Ry, min / π W 2 o, eff / λ, wherein F D is a dimensionless divergence factor having a value of 10 or greater.