The paper presents some model improvements for the optical simulation of laterally-corrugated ridge-waveguide distributed feedback lasers. Simulation results are discussed and design principles for achieving single-longitudinal-mode operation are outlined. The effects of the laterally-corrugated ridge geometry both on the coupling coefficient and on the Bragg wavelength of different transverse modes are presented. The improved modeling has been used to design 980 nm distributed feedback lasers with laterally-corrugated ridge-waveguide third-order gratings. The lasers fabricated using nanoimprint lithography exhibited single-mode operation with 50 dB side-mode suppression ratio.