We investigated the intensity noise spectra of a single beam of a pump-enhanced continuous-wave optical parametric oscillator (OPO), which was used to generate quantum-correlated twin beams, as a function of the pump power. With a triply (pump-, signal-, and idler-) resonant cavity, the oscillation threshold of our OPO was 8.5±1.3 mW and the measured slope conversion efficiency was 0.72±0.02. Twin beams with a power of 240 mW were generated at a pump power of 350 mW. The relaxation oscillation frequencies, which depend on the pump power, were observed when the pump power of the OPO was 12.5–28 mW. The experimental results confirm the predicted increase in OPO relaxation frequency with pump power. We experimentally inferred squeezing of the single-beam intensity, for the first time to our knowledge, by exploiting the nature of quantum noise that is dependent on loss.