1060 nm high-brightness vertical broad-area edge-emitting (HiBBEE) lasers with laterally inhomogeneous ridge waveguides are investigated. The effects of triangular, fishbone, and square-shaped corrugations on the loss of fundamental and higher-order modes are calculated by the beam propagation method. Lasers with 15 µm ridge width, 2 mm cavity length, and various types of corrugations are fabricated. The combination of vertical broad-area and fishbone- and square-shaped corrugations yields excellent beam quality, with beam quality factors M2 ≤ 1.5 and 2.6 in vertical and lateral directions, respectively. Despite the loss in output power due to the increased losses incurred by the corrugations, corrugated lasers provide higher brightness than the reference laser with a conventional straight ridge waveguide. HiBBEE lasers with square-shaped corrugated ridges provide 1.7 times larger brightness than the reference lasers.