A 25 dB reduction of resonant intensity noise spectra is experimentally demonstrated for both the antiphase and in-phase relaxation oscillations of a dual-frequency solid-state laser operating at telecommunication wavelengths. Experimental results demonstrate that incorporation of an intracavity two-photon absorber that acts as a buffer reservoir reduces efficiently the in-phase noise contribution, while it is somewhat ineffective in lowering the antiphase noise contributions. A slight spatial separation of the two modes in the nonlinear two-photon absorber reduces the antiphase resonant intensity noise component. These experimental results provide a new approach in the design of ultra-low noise dual-frequency solid-state lasers. (C) 2016 Optical Society of America