A thickness of at least one preselected portion of a substrate, such as glass substrate for example, is controlled. A laser beam is directed to the at least one preselected portion of the substrate in a viscous state, thereby increasing a temperature and reducing a viscosity of the at least one preselected portion of the substrate in a viscous state sufficiently to cause the at least one preselected portion of the glass substrate to attain a desired thickness. The laser beam after it is generated can be directed to a reflecting surface from which the laser beam is reflected to the at least one preselected portion of the substrate in the viscous state. The substrate can comprise a glass ribbon produced in a downdraw glass forming process for example, and the laser beam can be directed onto a plurality of preselected portions of the glass ribbon.