Experimental results are presented for the statistics of 0.6328-microm laser irradiance fluctuations for multiple-pass propagation through a laboratory-simulated atmospheric turbulence of strength C(2)(n) = 2.476 x 10(-11) m(-2/3) and the smallest scale size l(0) = 2.74 mm. The coefficients of variation gamma(0), skewness gamma(1), and excess gamma(2) of irradiance fluctuations are plotted as a function of path length. From the plots of gamma(2) vs gamma(1) for various values of sigma(2)(1) (= 1.23 k(7/6) C(2)(n)L(11/6)) in different regions within the turbulence, the following forms of the probability distribution functions for the irradiance fluctuations are considered: lognormal, Rice-Nakagami, m distribution, gamma (and exponential), and K distribution. We have also demonstrated the characteristic feature of -8/3 power law behavior of power spectrum and the shift of Tatarski's peak frequency in the case of strong turbulence.