We describe a new approach for improving the relaxation oscillation frequency characteristics of quantum-well lasers at the second quantized level. Applying an antireflection (AR) and high-reflection (HR) coating to the laser facets suppresses lasing at the first quantized transition and promotes it at the second quantized transition. The relaxation oscillation frequency for the laser emitting at the second quantized transition is twice as high as that for the laser at the first quantized transition. The increase in the relaxation oscillation frequency of the laser operated at the second quantized transition is mainly due to the increase in the differential gain. Furthermore, the differential quantum efficiency increases to 0.5 in the AR/HR-coated laser. >