The probability distribution p(n) for the detection of n photons emitted by a single-mode dye laser in a short time at various excitations is measured, together with the distribution of time intervals between pairs of detected photons. The first measurement yields the probability density P(I) and the moments of the light intensity I, and the second one the two-time intensity-correlation function. Measurements are also performed at three different wavelengths. P(I) is found to have a two-component structure, and the relative intensity fluctuations //sup 2/ grow, apparently without limit, as the excitation tends to zero, so that no thermal state is reached. A possible explanation in terms of pumping fluctuations is discussed. The correlation function has the form of a sum of three exponential functions, and the amplitudes and decay constants of the three components are derived. The effective decay-time constant exhibits a thirteenth-power-law dependence on frequency of the laser light.